Anybody know about where the next prime should be? - Page 2

David · 2002-08-23, 20:32

Quote:

How high is probability that we find prime somewhere bewlow M(13466917)?

Well, according to the status page: http://www.mersenne.org/status.htm, every exponent below 5283000 has been tested and double-checked. Adding up the total expected new primes in the chart for 5255000 through 15300000 gives 0.1171 (0.0001+0.0004+0.0032+0.0034+0.02+0.09). So the chance we find a new prime below M(15300000) is less than 12%. So the probability that M(6972593) is M(38) AND M(13466917) is M(39) is over 88%.

Angular · 2002-08-24, 03:45

Quote:

Originally Posted by David

0.1171 (0.0001+0.0004+0.0032+0.0034+0.02+0.09). So the chance we find a new prime below M(15300000) is less than 12%.

Since we are adding probabilities they are required to be rigorously independent. Therefore, my cautious side asks, are these probabilities rigorously independent?

David · 2002-08-24, 13:04

Quote:

Therefore, my cautious side asks, are these probabilities rigorously independent?

I'm not sure, but if you look at the entire chart you see that there is a total of 4.29 expected primes! So what I said above cannot be entirely correct. I should have just said that there are 0.1171 expected new primes below M(15300000), and left it at that.

wpolly · 2002-09-17, 13:09

I think that the next one is M(20481817), the one assigned to me....
The factor progress took me 3 days, but I can't get any factor less than 2^67. :)

2002-09-22, 05:20

Quote:

Originally Posted by Tasuke

there was a prediction for mid 10 million and one for the 13 million. The 13 million was dead on(something like a .3 million spread) So it is entirely possible that there is a 10 million one that has slipped through as a first time error, or has not been checked yet.

And I am one of the nuts checking a 77.9 million(2 actually)

Im checking 79299931

Deamiter · 2002-09-24, 08:08

Why?!?!?!? I mean, I consider MYSELF to be nuts enough to be going for the 10M prize, but the odds gotta be absolutely INSANE as long as there're smaller numbers out there! Lets just make math history and clear a bunch of numbers rather than taking blind shots at huge exponents (that'll be cleared in a fraction of the time with terahertz processors in ten years anyway. ) :D

zygote · 2002-09-25, 17:36

The evidence is overwhelming that the best chance to find a Mersenne prime is by checking the smallest untested exponent that is available. The empirical evidence supports this approach, and I believe there are also theoretical arguments in favor. Here is one way of looking at it:

By my count there are 13 Mersenne primes whose exponents are known to be within a factor of 1.2 of the exponent of the next smaller Mersenne prime. For example, M(2976221) and M(3021377) are both prime and 3021377/3976221 = 1.015...

If there are no as yet undetected Mersenne primes below M(13466917), it would mean in 13 out of 38 cases (about 34%) the next higher Mersenne prime can be found by increasing the exponent by no more than 20%. That works out to a 34% chance of finding a new Mersenne prime below M(16160300).

Of course that is just an estimate based on very limited data. It also ignores the fact that many of the exponents between 13466917 and 16160300 have already been tested and found not to be prime. However, I think it gives a good indication of why testing the lowest available exponent is the best strategy for discovering a Mersenne prime.

That is, of course, if you're not in it for the chance to win a large cash prize.

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2002-09-17, 13:09	#15
wpolly Sep 2002 Vienna, Austria 3·73 Posts	I think that the next one is M(20481817), the one assigned to me.... The factor progress took me 3 days, but I can't get any factor less than 2^67. :)

2002-09-24, 08:08	#17
Deamiter Sep 2002 3²×13 Posts	Why?!?!?!? I mean, I consider MYSELF to be nuts enough to be going for the 10M prize, but the odds gotta be absolutely INSANE as long as there're smaller numbers out there! Lets just make math history and clear a bunch of numbers rather than taking blind shots at huge exponents (that'll be cleared in a fraction of the time with terahertz processors in ten years anyway. ) :D

2002-09-25, 17:36	#18
zygote Sep 2002 7₁₆ Posts	The evidence is overwhelming that the best chance to find a Mersenne prime is by checking the smallest untested exponent that is available. The empirical evidence supports this approach, and I believe there are also theoretical arguments in favor. Here is one way of looking at it: By my count there are 13 Mersenne primes whose exponents are known to be within a factor of 1.2 of the exponent of the next smaller Mersenne prime. For example, M(2976221) and M(3021377) are both prime and 3021377/3976221 = 1.015... If there are no as yet undetected Mersenne primes below M(13466917), it would mean in 13 out of 38 cases (about 34%) the next higher Mersenne prime can be found by increasing the exponent by no more than 20%. That works out to a 34% chance of finding a new Mersenne prime below M(16160300). Of course that is just an estimate based on very limited data. It also ignores the fact that many of the exponents between 13466917 and 16160300 have already been tested and found not to be prime. However, I think it gives a good indication of why testing the lowest available exponent is the best strategy for discovering a Mersenne prime. That is, of course, if you're not in it for the chance to win a large cash prize.