mersenneforum.org exponents 42M-43M
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 2008-02-01, 21:51 #1 davieddy     "Lucan" Dec 2006 England 145128 Posts exponents 42M-43M The numbers of exponents just listed as available seem abnormally large - as if they had not removed the ones which have been factored.
 2008-02-02, 01:51 #2 ATH Einyen     Dec 2003 Denmark 2×1,567 Posts 56,915 primes between 42M and 43M. According to ftp://mersenne.org/gimps/factors.zip there are 34,650 known factors between 42M-43M (haven't checked if there are several factors for same exponent), so that leaves 22,265 unknowns.
2008-02-02, 10:22   #3
davieddy

"Lucan"
Dec 2006
England

145128 Posts

Quote:
 Originally Posted by ATH 56,915 primes between 42M and 43M. According to ftp://mersenne.org/gimps/factors.zip there are 34,650 known factors between 42M-43M (haven't checked if there are several factors for same exponent), so that leaves 22,265 unknowns.
And 23787 listed as available for LL testing.

 2008-02-02, 14:25 #4 ATH Einyen     Dec 2003 Denmark 2×1,567 Posts Its not that far off then, its probably 1522 exponents in factors.zip which has more than 1 factor listed.
 2008-02-02, 19:24 #5 davieddy     "Lucan" Dec 2006 England 2×3×13×83 Posts Here are the percentages of Mersennes factored by range: 0-15M: 63.54% 15M-17.5M: 62.59% 17.5M-20M: 62.87% 20M-25M: 63.04% 25M-30M: 62.67% 30M-35M: 62.64% 35M-40M: 62.41% It is hardly over-extrapolating to guess that from 40M-80M the percentage factored before LL testing takes place will be close to 62.5% (5/8). The corresponding % we have got for 42M-43M is 58.2% which is significantly lower than expected.
2008-02-02, 20:45   #6
davieddy

"Lucan"
Dec 2006
England

11001010010102 Posts

Quote:
 Originally Posted by davieddy which is significantly lower than expected.
To get a feel for what "statistically significant" is, consider
tossing a coin 40,000 times. The standard deviation in the %
of heads from the expected 50% is 0.25%.

 2008-02-02, 22:08 #7 S485122     Sep 2006 Brussels, Belgium 2×5×167 Posts Do not forget that earlier versions of the program Prime95 factored one bit higher... For the current range of exponents that would be up to 69 bits compared to 68 bits with version 24 of Prime95. That removes 1.5% of the difference. Jacob
2008-02-02, 23:15   #8
davieddy

"Lucan"
Dec 2006
England

2×3×13×83 Posts

Quote:
 Originally Posted by S485122 Do not forget that earlier versions of the program Prime95 factored one bit higher... For the current range of exponents that would be up to 69 bits compared to 68 bits with version 24 of Prime95. That removes 1.5% of the difference. Jacob
I assume that you are using the "fact" that the probability of finding
a factor between 2^68 and 2^69 is ~1/68 ~1.5%.
But this accounts for 1.5% of the 40% of exponents which have no factor
below 2^68, i.e. 0.6% of all the prime exponents.
The discrepancy is bigger than this.

David

2008-02-02, 23:37   #9
markr

"Mark"
Feb 2003
Sydney

57310 Posts

Quote:
 Originally Posted by ATH 56,915 primes between 42M and 43M. According to ftp://mersenne.org/gimps/factors.zip there are 34,650 known factors between 42M-43M (haven't checked if there are several factors for same exponent), so that leaves 22,265 unknowns.
According to the nofactor file there are 22,265 exponents with no known factor. So there is just one factor per exponent in the factors file.

It could be (& I really hope so!) that the excess exponents are not actually available for assigning, like the way TF assignments go back into the "available" column when they're completed, because the v4 primenet server couldn't handle the change to factoring cutoffs in prime95 v24.12 very well. Roll on PrimeNet version 5!

 2008-02-17, 11:11 #10 davieddy     "Lucan" Dec 2006 England 2×3×13×83 Posts Now that some of these have been allocated for LLtesting , can we now identify some of the 1500 which have already been factored?
 2008-02-26, 15:38 #11 davieddy     "Lucan" Dec 2006 England 145128 Posts 70 in the "factored" column for 42.0M-42.1M. Is this not further evidence that our suspicions are well founded?

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