exponents 42M-43M

[davieddy]

The numbers of exponents just listed as available
seem abnormally large - as if they had not removed
the ones which have been factored.

[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.

[davieddy]

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.

[ATH]

Its not that far off then, its probably 1522 exponents in factors.zip which has more than 1 factor listed.

[davieddy]

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.

[davieddy]

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%.

[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

[davieddy]

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

[markr]

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!

[davieddy]

Now that some of these have been allocated for LLtesting ,
can we now identify some of the 1500 which have already
been factored?

[davieddy]

70 in the "factored" column for 42.0M-42.1M.
Is this not further evidence that our suspicions are
well founded?