hi all
parallel use of p-1 and trial factoring
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george suggested to run a p-1 test and trial factoring test before
ll-testing an exponent in version 20.
The possible factors are approximately logarithmic distributed, that
means there are about as many 66, 67 and 68 bit factors in the same
range. But the calculating time increases exponentially. So a computer
spends about the same time in finding 68 bit factors than factoring up
to 67 bits.
So it makes sense to factor up that length, where P[finding a factor
with n bits] = n-bit-factoring-time / ll-testtime.
So testing up to 68 factors should not take more time than (1/34) of an
ll-test. Most of the factors are found in the first part of the test.
using the p-1 factoring we have the same situation:
Using a B1 value of 50000 finds more factors than continuing from 50000
to 100000.
Why can't we do first first the factorization up to n-2 bits (1/4) of
the trial factoring time, then start the P-1 factoring up to 1/3 of the
B1 value, after this, we can complete the trial factoring process and at
the end we complete the P-1 (using the save file od intermediate file).
(the parameters can be optimized)
If one person runs the whole test, it is also possible that the computer
performs the stage 2 during the night when the computer is not in use
and Prime95 can use most of the memory.
no 68 bit factors
-----------------
until now >210 factors are found for 10megadiginumbers and more than 280
exponents were factored up to 68 bits.
Some (about 7) 67 digit factors were found but none with 68 bits.
The value in the cleared exponent list is rounded to the next digit
round(log2(factor)) so that only factors >67.5 bits are declared as 68
bits and factors from 66.5 up to 67.5 bits as 67 bit factors.
But there should be about two or three 68 factors?
organization of p-1 factoring
-----------------------------
A lot of factors of exponents between 10000 and 1000000 were found using
the new P-1 method. Is there a database which contains which exponent
were tested using which B1 and maybe a database od the save files?
reto
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