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Old 2016-11-30, 02:20   #1
carpetpool
 
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"Sam"
Nov 2016

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Post Trial Divison Improvement

I also wanted to mention the trial division of numbers (of special forms) in PFGW for (a^n-b^n)/(a-b) (with prime n) for integer roots a, b should be reduced to only trial dividing numbers of the form 2kn+1 (or if it is faster, sieving values of 2kn+1 and then trial dividing). Although little interest is shown in finding prp factors of (a^n-b^n)/(a-b) other than the Mersenne Cofactors, I would strongly appreciate more and more searches for these factors from others. I am working hard at prp testing factors generalized base repunit forms, and a^n-b^n where a = b+1 more specifically. Thanks if someone knows how to do the trial division of these forms.
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Old 2016-11-30, 03:48   #2
paulunderwood
 
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From pfgwdoc.txt:

Code:
 -f[percent][[{Mod_Expr}][{condition}[{condition}...]]] 
      Modular factoring:
      -f{801} uses only primes which are of the form k*801+1
      -f{632,-1} uses only primes which are of the form k*632-1
      ** The {801} and the {632,-1} are the optional {Mod_Expr}
     *** NOTE new code added to do both -1 and +1. the format
         would be -f{801,+-1}   (the +-1 MUST look just like that)
      -f{256}{y,8,1) uses only primes which are of the form k*256+1 where
          the resultant primes are also of the form j*8+1
      -f{256}{n,8,1) uses only primes which are of the form k*256+1 where
          the resultant primes are not of the form j*8+1
      -f500{256}{y,8,1){y,8,7){n,32,1) uses only primes which are of the 
          form k*256+1 where the resultant primes are also of the form 
          j*8+-1 but not j*32+1.  There is also a 500% factoring level.
      -f{8132}{y,8,1){f,8132} uses only primes which are of the 
          form k*8132+1 where the resultant primes are also of the form 
          j*8+1. Also, all factors of 8132 (2,19,107) are checked first.
      -f{8132}{y,8,1){p,8133} uses only primes which are of the 
          form k*8132+1 where the resultant primes are also of the form 
          j*8+1. Also, ALL primes <= 8133 are checked first.
      Note this is also available within the ABC and ABC2 file formats, and
      within those formats, expressions can also be used.

Last fiddled with by paulunderwood on 2016-11-30 at 03:51
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