Unbelievable Mathematics

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Unbelievable Mathematics

#1  Postby Someone » Apr 09, 2010 1:41 am


!
MODNOTE
Off topic mathematical discussion continued from this thread.



This begins a sequence of posts by me without reference to what is said in the interim. Therefore, if there are opinions, questions, or comments, they should be held off until I announce that I am done with what I am setting out to do, which may be upwards of a day to completion. Continue with other subject matter between yourself and someone else, if you like. I will read that later, and I hope that I will not find that you have been badgering thin air with your remarks toward me.

The basic problem in the following quote from Calilasseia (the complete text addressed to me--with this new internet-forum style I'm learning interspersed--from a post first addressing someone else) is twofold in my opinion: 1) A jadedness towards extraordinary claims, and 2) Differing views on what should be taken as clear English, mathematics, and computer programming to the educated reader.

Calilasseia wrote:
Someone wrote:
Occam's Laser wrote:
Someone wrote:I'm sure there've been plenty of half-intelligent things said since I last posted, but I just want to add to the math post something I forgot to mention: 365 starts the tenth on the list. Even out of the context of all of the other coincidences I know, most discovered by me, this one big one is a challenge to really describe as anything wholly organically derived from the work of one mind using a computer. A non-mathematician wouldn't be qualified to even try, and I don't think there are mathematicians here, so I'll wait a while before reading to see if you've found one who can meet me head on. I'm looking into whether, or really to what degree, other mathophiles have also been mediating. It's a lot of work because of the novelty of the question, so I don't have time for a whole lot of BS here or elsewhere.

I am a mathematician, and I can verify that nothing you've said here makes any sense at all.


Then why didn't you?

Oh, I see one fallacy about my veracity is in question. I took the AHSME in years 1979-1982. My name is James G. Merickel. I received the highest 9th grade score in 1979. 105 was my score. 112 was the score of Noam Elkies, an eighth grader who skipped 9th grade and was one of the other three people who achieved 4-year National-Honor-Roll Status in years '79-'82, qualifying being a score of 100 or better.


Hmm, what a pity the online archives only go back as far as 1997 ...

Would you be the same James G. Merickel cited in this page from Vol 105, No.4 of The American Mathematical Monthly perchance?


I haven't done much, and you can find even less online.

Someone wrote:The mathematical statement I have presented is partially published online at Prime Curios at the bottom of the entry for 4. I don't have to do anything. A good mathematician with a modicum of programming ability would seem to want to check it and could do it him- or herself.


Hmm ... I'm still waiting for those precise algorithms I asked for ...


Asked? Try badgered, and what I said was unambiguous mathematical language dealing with an obscure type of number theoretical question. It was elementary, however obscure, and a little thought on what I could possibly have meant from a neither blinkered nor jaded perspective by Calilasseia--who is obviously smart enough--would have revealed a single simple statement.

Someone wrote:I could be assuming there are no old-Earth creationists without enough doubt to call themselves agnostic, but I think this is a strawman theistic position you're erecting to balance against your atheism.


The evidence available suggests that it is far from being a strawman.


The fact that Calilasseia apparently doesn't believe that such agnosticism exists, doesn't mean his experience is the last word. On the other hand, I haven't actually spoken to people one-on-one on much about the notions involved. All I have are things like the discussion of the Moon/Sun apparent-size coincidence in Leonard Susskind's The Cosmic Landscape: String Theory and the Illusion of Intelligent Design (referring to debate with friends).

Someone wrote:In the interest of making this easier, I'll rewrite the program I wrote to generate the result, and you can check it. This will take about a half an hour. Make that two programs, one for the list and one to input number and base for the checking of the facts beyond that, and it will take an hour.


Oh good. I can hardly wait.

Someone wrote:Here's the first program, written in PARI/GP, and the second you won't need for a while, but I'll get that to you shortly:
{
p=2;while(p,n=p;m=0;e=floor(log(p)/log(2));for(i=0,e,if(n%2==1,m+=10^i);n=n\2);if(isprime(m)==1,n=m;m=0;e=floor(log(n)/log(2));for(i=0,e,if(n%2==1,m+=10^i);n=n\2);if(isprime(m)==1,n=p;m=0;e=floor(log(n)/log(3));for(i=0,e,d=n%3;n=n\3;m+=d*10^i);if(isprime(m)==1,n=m;m=0;e=floor(log(n)/log(3));for(i=0,e,d=n%3;n=n\3;m+=d*10^i);if(isprime(m)==1,print(p)))));p=nextprime(p+1);next())
}

This will generate a list. The first number comes out in a few minutes on a fast computer, and then you have to wait quite a while for the second and so on. A newer model computer should get you to the 44th in the sequence in under a day. Of course, someone has to set up PARI/GP if nobody has it. Use the wikipedia article link, like I did.


That looks like execrable C code of the sort that would have led me to receive an automatic fail if I had submitted it in any of my classes. Don't you know the first thing about formatting programs in a readable manner?


The problem here really is that the English language applied to elementary number theory wasn't clear to Calilasseia. If there was a specific problem with the code in reality--which I remind the reader was written in more like in-class exam conditions (by my choice, as preferable to a) just leaving Calilasseia and others struggling with--or, more likely, continuing to ignore--my clear mathematical statement and b) my doing another three hours of work explaining steps)--then pray tell exactly what it was. The answer to the question is that I am only recently self-taught aside from one single-semester course taken about thirteen years ago and not used. In high school, I did not have anything to do with the two overcrowded computers we had, and I have known an older mathematics professor with a good reputation who actually acted almost afraid of computers. Getting into my full background is not what this is about right now, but that shouldn't be all that hard to picture if you know the breadth of mathematics and its history.

Calilasseia wrote:
Someone wrote:Cali--whatever: I calculated on my own that to the nearest star at 1g acceleration averages half the speed of light approximately.


Actually, at the end of a year of accelerating at 1g, you would have reached approximately the speed of light. Given that g=9.81 m s-2, and there are 31,536,000 seconds in a 365 day year, then an elementary calculation yields a final speed of 309,368,160 m s-1. However, since this is faster than the speed of light in vacuo, actual acceleration would become negligible by the time your speed had reached 299,752,000 m s-1 (which is a little short of the actual valid of c, namely 299,792,458 m s-1). Over the year during which you were accelerating, your mean speed would indeed be approximately 0.5c, but then the journey to Alpha Centauri would take 4.3 years. You would spend one year accelerating, 1 year decelerating to arrive at your destination, and 2.3 years coasting at a speed close to c, which means that your average speed for the duration of the entire flight would be (3.3/4.3)c, or approximately 0.767c.


This has been discussed at length, and for those who have followed what-all I and Calilasseia said and not been willing or able to correct either of us on anything here, :naughty:

Calilasseia wrote:
Someone wrote:I assure you I am not an ignoramus on science.


My above calculation suggests otherwise.


In the end, you disappeared. Your classical calculation was good enough to show both of us wrong in reality.

Calilasseia wrote:
Someone wrote:You placed an unreasonable demand on my time, and I fulfilled it.


The symbolic mess you presented above is even less decipherable than the Easter Island boustrophedonic script. I'm supposed to spend time trying to make sense of that?

Someone wrote:I expect that you will be saying that my calculations are correct but don't mean anything next.


At the moment, I'm still waiting to see a legible presentation of the precise algorithm.

Someone wrote:You're not qualified


I'm certainly qualified to judge the legibility of your code. Which is practically zero. Plus, I really love it when people claim I'm somehow "not qualified" to evaluate woo.

Someone wrote:and as Occam's Laser has proven he doesn't know bleep


Actually, he's established both here and at RDF that he's probably forgotten more substantive knowledge than you will ever acquire.


The fact that my clear English presentation of an unambiguous claim in elementary arithmetic was incomprehensible to everyone here is just evidence of lack of qualifications, but I'll grant either or both blinkeredness or jadedness as alternatives.

Calilasseia wrote:
Someone wrote:I suggest you look up someone like Imre Leader at Cambridge and tell him I said Hello and that I claim to have discovered using mathematics that I am the Anti-Christ, within some reasonable approximation.


Is this some sort of in joke that he'll appreciate, or will he regard this merely as facetious on your part?


Calilasseia made me pretty mad for me to have blown my identity for anyone to read like this. ;) Actually, this is just the trickiest thing to discuss. They all expect someone except for atheists, it seems. This subject will not go anywhere over the internet.

Calilasseia wrote:
Someone wrote:He'll check out my question on mathematicians mediating with me, hopefully, because it's going to be a pain in the ass.


Not half as much a pain in the ass as deciphering that modem line noise you posted as code.


And how exactly would he know that?

Calilasseia wrote:
Someone wrote:Edit: I don't need to sound as unfriendly as you, so I take back the negative implications of this post. If you turn out to be interested, you could possibly be objective. I see what you're doing generally, and it's mostly overkill against a lot of people who aren't reading what you say anyway.


I'm used to supernaturalists not reading the facts when those facts contradict their mythology-based wishful thinking, so if you think you're telling me something new, then you're not.


Like I said, I don't have to be as unfriendly.

Calilasseia wrote:
Someone wrote:Example: 151 (in base 10)=10010111 in base 2 and 10010111 in base 4 is 16661, so the number 151 could be said to translate into 16661 in going from base 2 to base 4, to use one of my favorite little examples. Holding base ten as the overall context, 151 is the first number (prime or not) to translate as primes from bases less than 4 to bases greater than it up to base 4 all three ways, and happens to also translate all three of the ways to base 5. 911 is one of the other primes generated.


Oh, I see now. What you're doing is the following:

[1] Select a prime number;

[2] Generate the digital representations of that prime number in different number bases, from base 2 to base 10;

[3] Take those digital representations, and treat them as completely new numbers in base 10;

[4] Test these new numbers to see if they are primes.

So, to take a simple example, let's take the number 5.

510 = 1012, 10110 is prime
510 = 123, 1210 is composite
510 = 114, 1110 is prime
510 = 105, 1010 is composite
510 = 56, 510 is prime
510 = 57, 510 is prime
510 = 58, 510 is prime
510 = 59, 510 is prime

Why didn't you say that in the first place?

You could speed this process up enormously by simple recourse to a large database of precomputed primes on a DVD-ROM. Which would be capable of storing 4.7 gigabytes of data, which would give you the first 293,750,000 prime numbers if you stored them as 128-bit integers (and you'd probably need to go all the way to 128 bit integer arithmetic to maintain precision whilst still maintaining decent computation speed). On a 32-bit PC, this would involve getting your hands dirty with multiple precision arithmetic routines. I'd sidestep high level languages for this sort of work and skip to assembler, because while it would take longer to debug, the end result would run a lot faster - you could speed up your code by a factor of 10 at least, and that's working with multiple precision integer arithmetic.


I do believe that Calilasseia disappeared at this point, pretty much. This is partially a change of subject from the coincidence that was provided. I am guessing that the implication is on the one hand I'm a computer nincompoop, and, on the other, the results could have been achieved by data-mining. I can't argue with the first.

Now, anyone who hasn't seen it should read the claims of the first post of the thread in this division entitled "List 3 Coincidences You Know Of (For Debunking?)" Here is something to add to that mix that was more recently discovered: In base 8, the whole part of (555+1/5)5 is the product of 22*3*5*7(=644=42010) and the prime 163171555655. 5558=365 (I disagree about the need to put subscript 10 here). More about the 365 stuff just before the end of this sequence of posts. This number stuff mostly (The last of of this series will begin by explaining 'mostly' a little bit) starts in my experience with the discovery (365+1/4)4=17797577732+72/28.
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Re: Fundamental Question To All Supernaturalists

#2  Postby Someone » Apr 09, 2010 4:20 am

In the first paragraph of what follows--the major part of the critical earlier post by myself--I provide the essence of my hypothesis for the nature of Earth's origins. The hypothesis is less robustly supportable at present (as one of various alternatives) than the idea that I am giving grounds to bring it back into the arena of plausible hypotheses. The first sentence is overblown. The point is not what I know about base-ten coincidences entirely, but the fact that they are now known beyond the point at which they should be (given the effort going into finding them); and they are strong enough to support claims of some form of signalling--at least a beacon-like "base ten has scads of coincidences"--from a higher intelligence. The second paragraph is that which was the major bone of contention of the last post. I'll break it down a little after you read or re-read the two paragraphs, and then I'll provide the specific outputs of the program so heartily attacked as unreadable by Calilasseia. In the third post of this sequence, I'll generate the proper data from the second smaller program that has yet to be repeated.
Someone wrote:The testable prediction I am making is that I know more about coincidences involving base ten than anybody on the planet, and a lot has to do with 365. On the seeding, same material as everything else in the cloud will do just fine if we're to get to a point billions of years down the road where the Moon and Sun look almost the same size from Earth and 365+1/4 is the approximation to the number of days in a year, and that's all we care about at the start. You can just do a lot of the rest by study of the life that evolves and some good nanotechnology operating subliminally on its sense organs. Getting things pretty precise at the outset does entail massive computing power, but you know you have to grant that. The fact is that I'm describing a co-adaptive system with life on Earth as much as a creative one. Not a whole lot goes into the signal, but it's enough. I got the highest 9th-grade score on the AHSME on the day the first magnetar was discovered.

Here's a little taste of the math: List the prime numbers that translate twice as primes digit-by-digit from base 2 to base 10 and do the same from base 3 to base 10. The 4th on the list is the first that translates once from base 4 to base 10 as a prime; the 44th is the first to do it twice; both start with 234 in base 10; and the 4th is special in that it translates twice also from base 5, doesn't translate as a prime again except for the tautology at base 10 until base 20 (Using 'digits' greater than 9) at which base it translates five times, with the next two bases for this being 22 and 25--4 and 2 times, respectively.


Okay, the first noun phrase of sentence two in reference to sentence one makes it clear that there is one list that must reasonably be inferred is in increasing order. Comprehension of the whole paragraph will then fall into focus on appreciation of this. The first sentence describes what the list is, and I would hope that at the very least after reading Calilasseia's revelation on the matter most people could figure that out. However, for clarity's sake, I will spell it out using a small number so that I can do this in my head here. Take 1310=11012=1113. 110110=100010011012 and 11110=111113. If 111, 1101, 11111, and 10001001101 (base 10) were all primes, then 13 would be on the list. If the entire statement is not now clear (along with Calilasseia's suggestion of using a database of primes for the research being wrong), then it soon will be with the following list and the next post.

Here is the list of the first 44 terms of the sequence:
1: 3660109, 2: 69664477, 3: 222606961, 4: 234099253, 5: 244425499, 6: 252362347, 7: 264492601, 8: 289353943,
9: 334710967, 10: 365431051, 11: 390680029, 12: 400817629, 13: 422451433, 14: 530917927, 15: 577666909,
16: 594302287, 17: 723691147, 18: 738084037, 19: 753950893, 20: 788894581, 21: 807284953, 22: 827671849,
23: 842959669, 24: 985296679, 25: 986511051, 26: 1187799427, 27: 1243788031, 28: 1417131259, 29: 1442128351,
30: 1461773629, 31: 1609808887, 32: 1718949343, 33: 1728686041, 34: 1779146671, 35: 1890591799, 36: 2018095633, 37: 2078547529, 38: 2124366697, 39: 2142242239, 40: 2173576177, 41: 2209776061, 42: 2211799081, 43: 2298824377, 44: 2348568403
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Re: Fundamental Question To All Supernaturalists

#3  Postby Someone » Apr 09, 2010 6:50 am

The following full-post repetition still holds true (EXCEPT FOR TWO THINGS I WILL HAVE TO CORRECT MYSELF), but I'll do a modification to generate the set of primes generated from a given member of the list (rather than just the count, c).
Someone wrote:I still don't quite know my PARI/GP well enough to write a program that prompts for an input. Take the first example that I give of what you should write for the second program to test the first number for number of times it converts from base 4 to base ten; and change n accordingly to find the fourth on the list to be the first that generates an output of 1 and the 44th is the first to generate an output of 2, and then go back to the 4th on the list changing b to get all those 0s (remember to skip 10 or you get an endless loop) until at b=20 you get 5, at b=21 another 0, 22-->4, 23-->0, 24-->0, and 25-->2, after which I don't think it was all that interesting. Here is the test generating 0 for the number of times the first on the list generates a prime in going from base 4 to base 10:

{
n=3660109;b=4;c=0;f=1;while(f,q=n;m=0;e=floor(log(q)/log(b));for(i=0,e,d=q%b;n=n\b;m+=d*10^i);if(isprime(m)==1,c+=1;n=m,f=0);next());print(c)
}


The first thing that needs to be corrected: 'n=n\b' should be 'q=q\b'. So, with that fix, the general case is handled with the above program modified by removing 'print(c)' and replacing 'c+=1' by 'print(m)' (All reference to 'c' is deleted) and the proper choice of n and b.

The outputs for b=4 are blank for all of the numbers listed in my last post except:
n=234099253 (the 4th term) spits out 31331001020311,
n=788894581 (the 20th term) spits out 233001121031311,
n=996511051 (the 25th term) spits out 323121120311023,
n=1417131259 (the 28th term) spits out 1110131323103323,
n=1461773629 (the 30th term) spits out 1113020032110331,
n=1890591799 (the 35th term) spits out 1300230002100313, and
n=2348568403 (the 44th term) spits out 2023333010331103 AND 13030003113231111331113133.

The outputs for the 4th term as b varies on up past b=4 (skipping b=10, as explained) are blank after starting with outputs of 434412134003 and 24104134001242003 for b=5 until b=20 gives 4332833, 172223, 12113, and 2063. I apparently made a mistake thinking there were five primes generated, when in fact there were four (This is the second of the things mentioned at the top). This cuts ever so slightly into the belief that this is a mighty strong coincidence in one way only to increase the nature of the coincidence--around the number 4--in another way. The output for b=21 is blank and b=22 gives 2197633, 98929, 9697, and 2017. b=23 and b=24 give blanks, and b=25 gives 2548003 and 73303. If there is anything at all remarkable going higher up with b, I would be surprised. Even the last part mentioned is barely worth it.

So the features of this coincidence that I discovered are spelled out to the extent I explicitly identified them. I doubt there is a best way to describe it, and I am quite sure mathematicians have not engaged in issues of coincidence internal to mathematics to the degree necessary to analyze it very well. I will be remarking in some way more on this coincidence
some time next week perhaps, but the rest of these posts are going to deal with other mathematical coincidences.

Edit (after five minutes of inhaling legal poison): The sense/belief that I have been mediating the various results is exemplified by the process that brought this coincidence out in full. Following my nose at the Prime Curios website http://primes.utm.edu/curios in order to find something to contribute, I found that thrice prime translation involving base 2 (to base 10, of course) was a rediscovery of mine (If I have it written down, I don't know where, and I would suggest anyone wanting that to just rediscover it also rather than hunting through the site (The number isn't too big)). So, after a few moments thought--realizing that 4 times might not be reasonably quick computing and might likely have been done already--I picked finding twice for bases 2 and 3. In concert with some other thoughts on what might be interesting, I decided on a list rather than just the first. The process of finding the results can be described as having this list come out, checking for the first that got a base-4 result, testing that for base-5, being pleased with that and hoping for more of the same with increasing disappointment until base 9, and then saying to myself that maybe it would continue negatively. I must have been riding pretty high by base 14 or 15, and then a sense of the absurd came over me. When I got to the base 20--and I did not use the program implied here, but one which just output one number to be replaced (explaining my error as probably a typo)--the result I got stunned me. Base 22 doing the same thing (except by the same I mean many, not four specifically) was a further shocker, and I included base 25 for a third more-than-one result. I kept going for quite a ways with no expectations and nothing interesting to see (I don't think). Only later did I see what happened with initial digits and with the positions on the list. I noticed something else I haven't even mentioned as significant first, and that's that the second one to give a base-4 result is all the way up at the twentieth on the list.

Incidentally, I certainly have not had time to investigate deeply the idea that other recreational elementary number theorists have mediated results, but I pulled back from my prediction on my own mediation being stronger than the collective work of others. I'd now say it's more likely that people who have read all of the curios at the above-mentioned website prior to my own and have read the book--the authors themselves, for instance--know more mediated details but couldn't come close to explicitly identifying them as such. I'm really not certain of this though. Where does natural work end and outside assistance begin? I would recommend not looking at anything before 2357 for a hint of what others might have mediated if there is anyone else interested in this, but I might have missed some things earlier on.
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Re: Fundamental Question To All Supernaturalists

#4  Postby Someone » Apr 09, 2010 10:26 am

I'm bound to get some sleep soon, so this will be a quick, short post on multi-base palindromes. This subject actually seems to me more ripe with the sense that other investigators were collectively blocked from thinking about it much than with my being pushed toward it, but that's not been thought out.

Example one: 4838419019 [correction edited in late] is the smallest number which is a 5-digit palindrome in four different bases, beginning with base 91. You'll note that it is almost the concatenation of two 5-digit palindromes in base ten, and that base fits as a part of the coincidence. I just recently discovered the factorization 7*691202717 is cute, as you can say that movement of one digit makes concatenation of palindromes in two ways for both this prime and the original number.

Example two: 3360633 is the first number which is a palindrome of length seven in three bases--9, 10, & 11. It is also 8th on the list someone else came up with long ago of palindromes in base 10 which are sums of the composite numbers up to some point, and 6th on the list is 33633. This is just the straightforward mathematics part of the result. The really strange thing was the discovery process and other stuff, starting with the apparent fact that the someone else concerned came up just the smallest bit short of the full discovery. I chose this number as the basis for the name Eegogee at the old forum. If there is any conversation later on, I may expand upon this.

Okay, after I get my post-sleep bearings, I'll talk about some more of this. Those are the big two on that particular subject.

Note: These are peer-reviewed items at OEIS.
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Re: Fundamental Question To All Supernaturalists

#5  Postby Someone » Apr 09, 2010 7:28 pm

Ok. I see there has been some continuity with previous conversation (or something). As I said, I am presenting details promised a week ago in a series of posts. This post continues where the last left off, with a palindrome of marked coincidence. This time--the first thing--the discovery is only a partial re-discovery. After that, I transition to the subject of things known prior to my involvement.

You can quickly find the details of the one that I partially re-discovered by going to the website I linked to in one of the overnight posts. The number is 98689, and my partial re-discovery was that this is the first prime which remains prime upon placing 1, 2, 3, 4, or 5 zeros between each pair of consecutive digits.

I have definitely found that others before me have certainly discovered some outlandish mathematical coincidences in base ten previously. Here is the biggest one that perhaps says something about how our digits are drawn: The largest power which uses no digit twice is the square of 99066 ( 9814072356), and the number of squares (not counting 1) of that sort is 609. The base ten also has the nice feature on this subject that 229--a much higher power than for any other small base--is of this type (though this seems barely worth mention).

Any mathematically informed reader will know the first ten digits of the base of the natural logarithms. In the context of all of the coincidences, the question can almost be raised as to whether logarithms are a 'natural' thing for mathematicians to use. In any case, I speculate that e=2.718281828... (It does not continue repeating) is the first real notable base-ten coincidence that was ever found, though defining that notability would be an outrageous task. On a related note, mathematicians will generally know the fact that log102=0.30102999... (and log105=0.69897000..., et cetera). These facts are enough or almost enough in themselves for a little bit of speculation on the true origin of our having gravitated in large measure toward base-ten usage.

At this point, I'm going to break and organize the next post. I recommend a look at the rather poor article (currently) http://en.wikipedia.org/wiki/mathematical_coincidences. You will find an additional nice one involving the reciprocal of 17 and perhaps a few others on base ten that I wrongly think of as insignificant. The article is mostly about other things which the reader may find interesting too.

Edit: Oh, yeah! While you're at the article, read the article linked to by the Noam Elkies I have earlier mentioned. It won't be easy-going for a non-mathematician, but it's well worthwhile. It's about 'why' the square root of 10 and pi are reasonably close to each other.
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Re: Fundamental Question To All Supernaturalists

#6  Postby Someone » Apr 09, 2010 10:25 pm

Anyone interested in my verisimilitude in the claim I make on the pace and nature of the discoveries listed in these posts can start dealing with that by looking at the following conversation. It's a continuation of a mathematics-reference-desk conversation. You won't be able to sort it out very much, but it stands as a kind of evidence. You might also learn some mathematics on a low level. Please do not disturb the person concerned. He's pretty busy. My talk page--which I have chosen to use in a way as my user page--says some stuff too, not all number stuff either.
http://en.wikipedia.org/wiki/User_Talk: ... Discovered
Here is one of the little coincidences--a connection of two re-discoveries. 82818079...321 is prime and 82000 is probably the only non-trivial number that uses only the digits 0 and 1 in bases 3 to 5. If you go to the link, you will see that I just received a message in regards to the first.

The following thread started out differently, but records pretty much all of the discoveries I have been and will be talking about. It is also the first public conversation thread I ever created AND the thread number is one off in one digit from being my 7-digit phone number. We can work out the closest thing to physical evidence of something or other that I can provide through this medium at a later date (i.e., someone like Calilasseia can call me). I'm currently identified as Eveneye--Eegogee--Julzes. My home space there is hopelessly out of date in tone if not detail, but of course you can read it if you want.
http://www.bbc.co.uk/dna/h2g2/brunel/F1 ... ad=6922123

The following thread is an alternative source for many of my coincidences and says some other interesting things (by me and others). I would suggest going in reverse order rather than reading the whole thread or trying to find my first post there based upon a poor guess of September for when I first showed up on it.
http://www.bbc.co.uk/dna/h2g2/brunel/F1 ... ead=369071

Since this last one's thread number is a little of a reminder (just the 71), my next post will deal with my accepted prime curios at the first site I mentioned in this sequence. I may make it the last one dealing with numbers other than 365 (That is, I will put everything else I can come up with in it, and there is a bit more). By the way, ever since I mentioned that Obama got 365 electoral votes (not the 'projected' 349 at that number's curio), my curios have been constantly rejected. I can't assume that's the or the only reason, but without an e-mail explanation I can guess that it might have been important.
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Re: Fundamental Question To All Supernaturalists

#7  Postby josephchoi » Apr 09, 2010 10:41 pm

what's your point though? That therefore god?
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Re: Fundamental Question To All Supernaturalists

#8  Postby Someone » Apr 10, 2010 1:56 am

A reminder that I will only be reading what is said in the interim after I finish all of these posts.

First a note of correction: My most recent submission to the Prime Curios site, 126704222713 being the smallest prime p such that the sums of the nth powers of all the primes up to and including p for n=1 to 6 are prime, has been accepted. Whatever was preventing the acceptance of others might be gone or have been misinterpreted. Now I'm guessing the prof wants proof of more technical facility from me rather than freaky stuff. Who knows?

Now, I'll start with the second largest of my accepted submissions. It's the analogue of 82818079...321 in base 7. The base-ten value of the starting number is 373, i.e. the prime is 1042104110401036...3217. I hadn't even previously considered this as in any way having to do with base-ten coincidence, but it does tie in a little bit since 73=343. It also offsets nicely from the one coincidence on 151 (in the quote of the first of this series toward the end), though they are hardly related except as minor parts of something more general about palindromes in base ten.

Now, I said 71 reminded me, so I'll look at one of the two submissions on 17. The one that reminded me is that the number of ways that 71 converts to a prime in going from smaller base to larger with larger base no greater than ten is 17, and this makes 71 a record-holder up to a very large number (I've repeatedly asked that my parenthetical on that curio be removed since almost immediately after submitting it, in case you read it, because it's bound to be very wrong). The other curio is a whole complex of stuff, really, that I will save till after I've covered everything else.

999779999159200499899 is the final 21-digits (with 12 nines) of 9999, and is prime. Along with this goes the fact that the first occurrence of seven consecutive digits six of which are the same, excluding terminal 0s from consideration, in a listing of the numbers nn is the string 5555575 at the very middle of 9696.

The curio on 4500 is a little interesting but need not be repeated. The more interesting thing to me about it is that I am (and was when I discovered/submitted it) 45 years old.

The curio on 5 is not particularly anything relating to base ten except that I found it after seeing a curio on 100. The fact that nobody before me apparently submitted it is what is surprising there. The curio is that both (prime(5))!/5!+1 and (prime(5!))!/(5!)!+1 are prime, prime(n) being the nth prime.

The curios on 73 and 173 are scarcely base-ten coincidences separately. They make a tiny impression, but when I get to the next post [I decided to put off the 365 stuff and focus on this 'complex' in the next post], if you have read them, you will see what that impression is. Not all that important. The curio on 1000 is a part of the complex entirely, so I'm saving that; 2437 doesn't seem to have anything directly to do with coincidences, but is merely research submitted and accepted; 17769643 is good nice research, but explaining how (at all) it's a coincidence to me is something I'm apt to mention in passing in the last of this series of posts; the 140-digit one is a part of the complex of results; and 0 is purely a mathematics statement about definitions that was accepted. So discussion of the complex of results is what I'll be doing after a brief relating of a few of my other discoveries and things I've come across (generally the former) .

On palindromes again briefly, the first prime over 1000, 1009, is the smallest number which is a 3-digit palindrome in five different bases, and the smallest number k for which a prime of the form k*2n-1 is currently not known, 2293, is the smallest palindrome of length 5 in two different bases. 1001 appeals to me as the product of three consecutive primes, but whether you make of it a coincidence of any kind is another matter, and it's no discovery. And the fact that 41041, 410041, and 101101 are all Carmichael numbers is something I can't even begin to appreciate, but I mention it since I have it written down on this short list in front of me.

Just a couple more, and then I'll go back to the complex of results. A discovery of mine that was not accepted at the Curios site was that 231661 reads as a prime beginning with base 10 all the way through base 22, excepting base 20. It's the smallest number/string that reads as a prime through base 16, and the smallest that reads as a prime through base 20 is over a thousand times larger.

I'm currently researching beyond a nice coincidence I really have to describe clearly now. If you take four distinct numbers, then there are 12 ways of concatenating pairs. In researching a very specific question, I got a rather remarkable result. The question is what are the record-setting collections of four consecutive primes in terms of the number of ways out of the twelve ways of concatenating pairs that are prime. Well, there is bound to eventually--I think--show on my computer screen a collection that generates ten, but the one generating nine is cool. This is what I'm submitting to Prime Curios right now: "5608951: The first collection of four successive primes giving as many as 9 out of 12 primes by concatenation of pairs is 100 times this prime plus 3 times the 7th-10th primes. The remaining three concatenations are all semiprimes."
Since I will need to send an e-mail along with it, the next post will be about the complex I keep referring to. I should be done with all of this in about 8 hours (I think).

Edit: I entirely forgot an interesting/strange one and something neat on 42 in conjunction with base 10; and I'm sure I have others not having to do with the topics of the concluding posts, but I'm just going to add these.
A. 367434 is the first base in which 21, 321, 4321, 54321, and 654321 prime, and 7654321 is also. This base is II0I27, the 7-digit left-truncatable prime with the smallest digit sum for it is 5132491, this read as base 10 is 3209736, and 3209710=1(100)1136 (By the way, 1001 was found by me--on someone else's list--to be the 136th product of three distinct primes shortly after this whole thing, and my father's d.o.b. is 3 January 1942). The first base for up to 54321 being prime is 4578=AI456, among other things.
B. The smallest prime which splits digitally in some base into three primes so that the other five arrangements are also prime is 4201 (in bases 3 and 9 both) and the smallest in specifically base 84=2*42 is 41999. To be clear about what is meant, 11437 is the number for base 10 as 11743, 43117, 43711, 71143, and 74311 are all prime. This last example is one of the ones rejected. (Oh, well!)

Edit II: I just looked at the details of something. Worthy of mention is the new result by Eric Weisstein: 377653776437763...321 is the second (highly probably) prime in the sequence with 828180...321, and it has 177719 digits.

Edit III: For the curious who are willing to do some work on what-all I can think of, one more thing came up. Look at the 16th-18th members of http://research.att.com/~njas/sequences/A171134 and then look at the similar stuff in the sequence of factorials (noticed by many, I'm sure).

Edit IV: Here's something else--two similar problems:
1) For what numbers a and bases b is (b-a)a a palindrome with digit sum b?
2) For what numbers a and b is (a+b)a-a(b-a)=b?
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Re: Fundamental Question To All Supernaturalists

#9  Postby Someone » Apr 10, 2010 6:45 am

Now, it's already much too late to contemplate finishing in the time-frame most recently mentioned, and I'm beginning to get tired anyway. So, I'll go to sleep after this description of the 'complex' of results that I have in mind, and then I'll spend all of tomorrow (today) until I feel I've really laid out as much as I can here on the nitty-gritty of the subject, an entirely different complex of results and some closing remarks. Then for a week at least I'm going to be doing very different things (I long ago committed the week starting Sunday to trying to help edit some of Wikipedia's more contentious articles, and I have much else to do as well).

Rather than spell everything out long here, I'm just going to refer to a sequence I re-discovered (most of) at the start of all this and my own published sequences on the complex; and then after mentioning one unpublished likely prime and a cute thing involving letters and the English language that will segue into what I plan to say later, I'm going to bed.

The re-discovery is http://research.att.com/~njas/A096594

The overarching sequence, and the source of the other curio on 17 is:
http://research.att.com/~njas/sequences/A173189

The first two sequences of mine are:
http://research.att.com/~njas/sequences/A152396 and http://research.att.com/~njas/sequences/A152397
The latter, by the way, is very hard to get a 5th term on.

http://research.att.com/~njas/sequences/A172998 is a little superfluous, but it connected me to the word thing.

I'll be editing in at the end another sequence which I forgot to bring the number for that's significantly related.

Now, the one likely fact that deserves to be included is that the next prime like 1000999998997996995994993 is 7777 digits (coming from 10972).

The thing involving letters starts with my looking up the curio on 10987. It's an alphametic: ALI+BABA+WAS+A=LIBRA. Trying to find something similar with 100999897 was what, therefore, occurred to me. The three 9s in a row told me I was looking for something of a slightly different sort, so I 'decided' it must be an anagram using letters spaced as the digits. At first, I both goofed finding something that was wrong and missing the right one: WE EXCEED W being the wrong answer (unless there's counted the space from Z to A), and GO OFF MOON being the right one. That's the transition point.

One other thing is that the sequence I referred to as 'over-arching' gave me a little gift as I was leaving by necessity on Tuesday at a certain time and the term for base 133 came out as 13 just in time before an automatic update that I wouldn't have been able to stop would have shut my computer down at a loss of that particular piece of weeks' worth of research.

Edit: Here is the other sequence: http://research.att.com/~njas/sequences/A172994
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Re: Fundamental Question To All Supernaturalists

#10  Postby THWOTH » Apr 10, 2010 6:50 am

Yeah, but is three the perfect number?
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Re: Fundamental Question To All Supernaturalists

#11  Postby Someone » Apr 10, 2010 7:51 pm

Okay, I plan to finish this sequence of posts in just about fifteen-and-a-half hours (probably 14 from when this gets posted). I won't be available for meeting direct responses to the sequence for quite a while thereafter, but I may respond tomorrow to some things said since I started. I remind people that some of what I have said in this thread goes back to near its beginning.

Now, I have to begin with personal narrative. I expect to fit some of the 365 stuff in this post at the end, but it's the next one that will be more technical (and it will have bizarre testable real-world claims).

I skip most of my life to get to 23 April 2004. Sitting outside the Univeristy of Pennsylvania bookstore, I was thinking about the plausibility of writing something on the notion that societal obstacles to human immortality are larger than scientific and technical ones. For some reason, I had the egocentric notion to imagine that I might be given a specific fraction of then-living humanity that would be immortal--perhaps with cosmological limitations--by a super-intelligent predictor, so I reasoned out a guess of the maximum possible and then picked (Nobody was talking to me, and I don't and didn't believe what I'm saying to be likely, so you could put this as a highly unlikely semi-delusion) 76.32%. Later that night, looking at the full Moon (Hey, I'm going on memory--tell me if I have my date wrong), I added the digits 85 and determined that I might be off by exactly 100 years due to personal optimism, and I now think 50 years is most likely of the three very unlikely possibilities (Then again, maybe there is more pessimism about the possible rapid change that is needed than there should be). How I got to this point is by a strange logic about my own logic. To complete the thing, I posited that three more digits would be found by someone else 'In Judgment', just thinking about how precisely the thing could be nailed down. :crazy: :lol: :scratch: Anyway, it's not theoretically impossible to have such a positive percentage.

A little over a year later, I broke out of a bit of a depression on 31 May with the thought that I hadn't moved things forward myself, whatever the possible best future may be. Several (about ten) days of blank-but-serious thought on the matter led me to pick up on some of my old thoughts about society's arrangement. In particular, I had decided I favored three couples joining together to form a larger-than-traditional family core, so I thought to calculate what thirteen-factorial was (for some reason) and got a by-hand over-calculation (for some reason), and I very quickly (somehow) wrote down The Miracle Scheme you can find in shortest form at both my Wikipedia and h2g2 spaces (See one of the earlier posts for links). This topic (and Ralph Nader! :lol: ) will be discussed more at the very end of these posts (partially on the instigation of TMB, someone else who has been on this thread recently).

A bunch of other crap happened (some of it like the Boxing Day Tsunami which already had, and some more personal) after this and before I was 'given my explanation' while reading Robert Oerter's The Theory of Almost Everything. I grew up knowing I had some strange things in family birthdays. The ten-date coincidence I have identified is posted at the start of the thread 'List 3 Coincidences You Know Of (For Debunking?)'. The core of it is the sequence 6 July 1964, 16 July 1964, 6 August 1964, and 9 August 1965, the birth dates of myself followed by those of my three closest same-generation relatives, for whom I provide the sole link. The explanation I refer to is that 16 July 1945 was defined for its meaning by a reading of the book in question, my having missed the fact (somehow) up to that point in my life. To save space and time, I direct the interested reader to the thread named. For anyone not that interested, the finding immediately provoked the calculation (365+1/4)4=17797577732+72/28. A much later calculation (on 03/06/09, USA reckoning) was (365+1/4)2=37*61+9/16, and most recent on the subject is the one from base 8 that [(555+1/5)5]=22*3*5*7*163171555655 (I'll see if there's anything cute surrounding the fractional part, but if there is I don't see it right now).

I'll pick up in the next post where this one leaves off.
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Re: Fundamental Question To All Supernaturalists

#12  Postby THWOTH » Apr 10, 2010 10:50 pm

Oo, can't wait.
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Re: Fundamental Question To All Supernaturalists

#13  Postby newolder » Apr 10, 2010 11:03 pm

:popcorn:
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Re: Fundamental Question To All Supernaturalists

#14  Postby Someone » Apr 11, 2010 5:37 am

I wasted time on baseball today, so I'm clearly going to need another full day here. Wikipedia and the other stuff can wait for me to make this all as coherent as possible. I break at the end with a sequence. At first it was only the shocking thing called by me my 'Weird Arithmetical Leap'--the very last line. The penultimate line is what I looked at second in that sequence. Look at its final eight digits to see what I saw in the order I saw it (after reading through what follows). I'll try to clarify things a little bit before I go to take care of a morning chore I have every Sunday and then come home to go to sleep, and then I'll pick up again around 6PM my time with whatever I've left out that I feel is urgently in need of fixing, including the conclusion. Then before I go to sleep around dawn Monday morning my time, I will read whatever I've been missing here. That should work as a solid schedule. It better, because I do have other things I have to do.

What I say from here to the dotted line is coincidental stuff on 365+1/4 that is subordinate to most of what I have to say. Explaining it all is something I certainly wouldn't have space or time for here, even if I were finished, which I'm not; but I put it in anyway for anyone who really has a lot of time to kill and some mathematical programming skill.

Anyway, the first of those three calculations given leads to a lot more stuff in a purely mathematical way but also another strange--very strange--way. But there are also other things. 365+1/4 is 111112+1/11 in base 3, for example, as someone called Gnomon over at h2g2 pointed out to me. This is just one of the not-fully-explored subjects I'm concerned with in this general area.

One of the purely mathematical (coincidental) things is that the number 17797577732 when a factor of 4 is removed gives a number that has five of its ten digits as 4 and the sum of this number's divisors is similar, as a non-trivial pair. I just throw that out there and move on.

Another thing is that one can make a nice sentence describing features of the left side of the first equation to get 642 (the first 6 digits with an extra 4 replacing the 2), and the digits that count themselves in the right side can be lined up as this number's largest prime factor. Again, just tossing that out.

A bigger thing is that the sums of the digits of the numerator and denominator of the fractional part are both 13 and the numbers leaving remainder 13 upon division by 16--a divisor of 32, the final digits of the whole part--in place of 365 generate the same fractional part. This raised for me a narrow question in looking for similar results with the 11 in 365=11*32+13 being sought to be 13 also. I spell this out with the two results I found rather than spelling it out formally, though I can do that (It's just quicker than either looking up what I wrote elsewhere or re-generating it).

1) (13*96+13+1/4)4=2530490533596+49/256
2) (13*672+13+1/4)4=5859806899008672+49/256

It's just unusual, this last thing. A part of something I called my '96 Coincidence', to start with. No space or time here.
----------------------------------------------------------------------------------------------------------------------------------------------

Back to the narrative, which will skip a lot.

At some point a few months after making the key calculation--I call (365+1/4)4=17797577732+72/28 'The Main Fact'--I noticed that 1779 and 1914 in The Main Fact look a bit like dates of some significance. I recognized 1779 at first as the middle date of the USA's War of Independence, and I recognized 1914 for a couple of things you should too (I'm just saving time here). At some point much later, the thought crossed my mind that no matter how strong an argument I could make on the idea just using these dates (You should make a list of everything you can find that pops up on 1779 in particular, if you have time (and interest, of course)), I wouldn't convince myself much less anyone else. Then, at 3AM on 11 September 2008 the thought to do something strange that might generate more dates crossed my mind (for some reason). The first thing I noticed was that the fourth root of 17797577777.77777777777777777777 (twenty 7s after the decimal point--I'll explain soon) minus that of 17797577777 has first date 1776, and this was after first having looked at but been unimpressed by the second fourth root by itself. I still don't have any particular notions about the second fourth root, but the first by itself--what I looked at after checking the subtraction--did make an impression. What that impression was will come shortly. But first:

All data discussed in what follows are specific to the Microsoft Calculator for Windows 98 and Britannica 2001 on CD. These are the tools I was using at the time, and what I'm suggesting is that the programming of the first, the content of the second, and my activities generally are the major sources (at present) for indication of the semi-programming I have been alluding to. The way in which a choice of calculator matters has to do with the limits to the number of digits of input and output and vicissitudes of numerical analysis involving the accuracy of final displayed digits in subtraction of nearly equal terms. The suggestion here, soon to be stongly supported, is that the choices among various options in numerical analysis were manipulated from outside as a microcosm of what has been done generally (at least to form some coherent story).

The part involving subtraction (where I actually see the final digits) in the following actually comes late in the personal narrative, but I'm abbreviating.

The limit of the calculator's input gives 17797577777.77777777777777777777^(1/4)-365.25 as:
1) 2.33886071957018637575837077771024*10-7 when two square roots are employed, and
2) 2.33886071957018637575837077777117*10-7 when exponentiation to 0.25 is.

I believe the first three 7's in the two 8-digit final strings are the limit of accuracy. At any rate, having started with 1779, the 1863 was immediately the middle of the USA's Civil War to me, and 1957 was Sputnik I. The choice to pair these together in the search of Britannica yielded among the 20 outputs "Baha'i faith" and this--for reasons I will hold off on describing--prompted a further search of "Baha'i" giving 19382 hits, my 5-digit zip code, the zip code system having been instituted the year before my birth and my having moved to where I live now (for the second time, though the phone-number thing actually involves the number I first knew as a child--it moved with my step-father) in 2004. A check of 1938.2 as a point in time between two days in the common calendar (Remember that I was doing this on 11 September) reveals significance--consider it the beginning of World War II.

Now, consider the sequence obtained by subtracting instead the 4th root of 17797577777, with the number of 7s after the decimal point of the number inside the first fourth root varying from 1 on up to the limit 20. Consistently using the square root doubly as opposed to exponentiation to 0.25 and removing the decimal point and exponent on the result yields the following:

359142973499977410591576151215843
395057270849392473856631538710468
398648700584328153405196202589402
399007843557821663092273262750709
399043757855171013478303172156007
399047349284905948511079385487618
399047708427879442014298739340673
399047744342176791364620092250138
399047747933606526299652222141233
399047748292749499793155434507463
399047748328663797142505755849039
399047748332255226877440787079278
399047748332614369850934291543726
399047748332650284148283641489637
399047748332653875578018575618945
399047748332654234720992072586325
399047748332654270635289420821396
399047748332654274226719164856657
399047748332654274585862127762492
399047748332654274621776424874732

Okay, the next post is going to be talking primarily about the interpretation of a small number of second-millennium dates in this, but notice the absence of certain digits in the final digits of all of these. That continues pretty far in a certain way, and that is the very first thing I will remark on in the next post.
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Re: Fundamental Question To All Supernaturalists

#15  Postby Someone » Apr 11, 2010 6:49 am

Despite what is said at the top of the previous post, I've decided getting three hours of sleep now, working on this starting an hour-and-a-half after I wake up until the baseball game, going to sleep on my preferred schedule of 6:30PM to 1:30AM, and then doing as much as quickly as I can to finish this off on Monday is the proper path to take. Nothing more here till about 8 hours from now, I'd guess, and then two posts before the game and nothing for the rest of the day.
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Re: Fundamental Question To All Supernaturalists

#16  Postby argumentativealex » Apr 11, 2010 6:53 am

OK, guys, try to get some sleep - could be a long day tomorrow...
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Re: Fundamental Question To All Supernaturalists

#17  Postby Someone » Apr 11, 2010 4:50 pm

The following quote from earlier is apropos of the values given by the Microsoft Calculator for Windows98 of 17797577777.77...71/4-177975777771/4, the 7s after the decimal point ranging from 1 to 44, where the calculations were motivated by the fact that (365 +1/4)4=17797577732+72/28. Details on further parts of this motivation are earlier on; I'm just placing this up front.

Someone wrote:The string made up of 'final' digits for the first 44 terms is 38297838339867556722539777859777712092576764. Somewhere I did continue this further and I believe there was something else interesting; but I identify as anomalous the facts that a) 3 digits don't appear until after the 33rd term, b) the last of these is 4 at the 44th term, and c) 7's are highly clustered together. Also, the fact that zero is one of the three digits missing for a while helped me to notice this at all; in fact I probably would not have if, say, 6 accompanied 1 and 4 instead of 0.

Now, I won't even touch the 7-clustering anomaly here; that's already way out there (and harder to get a precise number on). I am going to get overly specific, and there is a fault with this, but... (If someone happens to be here who wants to do this 'right', be my guest). Consider the following an illustration. It could be construed as prejudicial. Probably neither those who understand it nor those who don't will like it.

The probability that a random string of digits will lack 0, 4, and another digit through exactly 33 terms and will have 4 come in as the last digit at the 44th term is slightly less than 8*(0.7)33*(0.2)*[(0.9)9-(0.8)9]*(0.1)=3.1320143281657361052*10-7 (just expanding it to a year I see--1052 has something to do with Buddhism(See term 8 of last post)). The leading 8 chooses what the other digit will be, and 'slightly less' comes from the next factor needing an adjustment to deal with cases of more than three digits, just to clarify for those who could almost but not quite get it.


Be careful to repeat the specific way this is calculated as described in the earlier post, if you are going to verify the data. Note that this one thing does have a much broader context as related in earlier posts here (and beyond that). Coming up late here is going to be a difficult go for any person qualified. I'm sorry about that.
Last edited by Someone on Apr 12, 2010 2:58 pm, edited 3 times in total.
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Re: Fundamental Question To All Supernaturalists

#18  Postby THWOTH » Apr 11, 2010 5:02 pm

    51 55 23 15 31 27
    09 10 14 45 30 49
    01 07 13 36 02 08
    17 20 37 39 16 26
    32 03 46 04 50 12
    33 38 54 43 06 53
    25 42 47 48 22 19
    28 40 35 21 24 05
    41 34 44 18 11 52

I rest my case.
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Re: Fundamental Question To All Supernaturalists

#19  Postby locutus7 » Apr 11, 2010 5:04 pm

God = Square root of -1. I rest my case as well.
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Re: Fundamental Question To All Supernaturalists

#20  Postby Rumraket » Apr 11, 2010 5:22 pm

THWOTH wrote:
    51 55 23 15 31 27
    09 10 14 45 30 49
    01 07 13 36 02 08
    17 20 37 39 16 26
    32 03 46 04 50 12
    33 38 54 43 06 53
    25 42 47 48 22 19
    28 40 35 21 24 05
    41 34 44 18 11 52

I rest my case.


Clearly wrong, mine's better:

    39 33 01 03 19 05
    87 98 92 23 18 27
    89 85 91 14 80 86
    95 08 15 17 94 04
    10 81 24 82 38 90
    11 16 32 21 84 31
    03 20 25 26 00 97
    06 28 13 09 02 83
    29 12 22 96 99 30
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