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rogue · 2017-01-21, 19:19

CRUS is not the only user of srsieve. if CRUS chooses to use another program or some older version of srsieve, it is their choice.

I have posted an updated version of srsieve here. Here are the release notes:

Code:

  Rewrote code to find algebraic factorizations so that more can be caught.  It will search for:
     GFNs -> where k*b^n+1 can be written as x^m+1
     Trivial -> where k*b^n-1 can be written as x^m-1
  which will remove all terms for the sequence.

  These algebraic factorizations are now written to algebraic.out so that they can be verified with pfgw:
     where k*b^n+1 can be written as x^q*y^r+1 and r%q=0 and q is odd
     where k*b^n-1 can be written as x^q*y^r-1 and r%q=0
     where k*b^n+1 can be written as x*2^m+1 and m%4=2
     where k*b^n+1 can be written as 4*x^z*y^m+1 and z%4=0 and m%4=0

Note the second section. One can now verify the algebraic factors found by srsieve. I have run a few tests and haven't found any bugs, but that doesn't mean that there aren't any, but they will reveal themselves when running algebraic.out thru pfgw.

In this new release, it is smart enough to deteremine if k and b have the same root, i.e. k = m^x and b = m^y so that it can more easily identify GFN and Trivial forms.

For the first two forms, those algebraic factors are not written to algebraic.out. For GFNs, it doesn't mean that it has a factor, but that if you truly want to sieve GFNs, use gfnsieve, not srsieve.

For the first two forms logs to algebraic.out, it factorizes k and b and can find factorizations where they share a common factor. The previous release could not do that.

I suspect that the last two might have some generalizations, but I haven't investigated.

If Serge or others discover additional algebraic forms, please share and I will incorporate as best I can.

2017-01-21, 19:19	#32
rogue "Mark" Apr 2003 Between here and the 19·373 Posts	CRUS is not the only user of srsieve. if CRUS chooses to use another program or some older version of srsieve, it is their choice. I have posted an updated version of srsieve here. Here are the release notes: Code: Rewrote code to find algebraic factorizations so that more can be caught. It will search for: GFNs -> where kb^n+1 can be written as x^m+1 Trivial -> where kb^n-1 can be written as x^m-1 which will remove all terms for the sequence. These algebraic factorizations are now written to algebraic.out so that they can be verified with pfgw: where kb^n+1 can be written as x^qy^r+1 and r%q=0 and q is odd where kb^n-1 can be written as x^qy^r-1 and r%q=0 where kb^n+1 can be written as x2^m+1 and m%4=2 where kb^n+1 can be written as 4x^z*y^m+1 and z%4=0 and m%4=0 Note the second section. One can now verify the algebraic factors found by srsieve. I have run a few tests and haven't found any bugs, but that doesn't mean that there aren't any, but they will reveal themselves when running algebraic.out thru pfgw. In this new release, it is smart enough to deteremine if k and b have the same root, i.e. k = m^x and b = m^y so that it can more easily identify GFN and Trivial forms. For the first two forms, those algebraic factors are not written to algebraic.out. For GFNs, it doesn't mean that it has a factor, but that if you truly want to sieve GFNs, use gfnsieve, not srsieve. For the first two forms logs to algebraic.out, it factorizes k and b and can find factorizations where they share a common factor. The previous release could not do that. I suspect that the last two might have some generalizations, but I haven't investigated. If Serge or others discover additional algebraic forms, please share and I will incorporate as best I can.