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Old 2003-05-30, 17:51   #4
smh's Avatar
Oct 2002

29·41 Posts

Prime95 trial-factoring is orderly.
I'm not sure about this. I remember from the old days that the client used 16 passes while trail factoring. I believe those 16 passes are still in there.

The program does however try all numbers below a bit length before moving to the next though.

Below is a message from George to the mersenne mailing list on 08 may 1996

Hi all,

David M. Einstein writes:
> I see that your new version is facoring in two passes. I assume that
> are numbers +-1 mod 8.

Your guess is correct. For those of you wondering why this is a
good idea - consider a one pass algorithm that first clears every
3 mod 8 and 5 mod 8 sieve bit. Then you clear every 3rd bit, every
5th bit, etc. Well, half the time you clear a bit because it it a multiple
of 3, 5, 7, etc. it was already cleared because the factor was 3 mod 8
or 5 mod 8. The two pass approach avoids this waste by using
two sieves, one for the 1 mod 8 factors and another for the 7 mod 8

> Would it be worthwhile to do it in 16 passes with numbers
> +-1 mod 8, +-1 mod 3, +-1,2 mod 5, or even in two stages say first seiving the
> interval from 0 to 8*3*5*7*11*13, and then seiving the residue classes found
in the
> first pass mod the other primes before 'trial dividing', or would the cost of
> reinitializing the seive be too great?

Good idea! It's already on my to-do list. If I remember correctly, 20% of the
spent factoring is attributed to the cost of sieving. Thus going to a four pass
approach would save 1/3 of 20% or about 7%. A 16-pass approach would save
a total of 9.3%. The cost of reinitializing the sieve is not that great. As
was pointed
out earlier, doubling the factoring speed results in a 2% overall improvement,
this item is not high on my priority list.

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