mersenneforum.org > Math Last part of P-1 puzzle ( in CRUS world)
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2017-07-30, 13:40   #1
pepi37

Dec 2011
After milion nines:)

2×709 Posts
Last part of P-1 puzzle ( in CRUS world)

Since in my last post everyone told me to be patient ( until I found big prime) I decide to solve last part of puzzle of P-1 that is missed to me.

So Batalov say this

Quote:
 P-1 is effective for the inputs that have a known partial factorization of all future factors. A trivial example is Mersenne primes, as well as Wagstaff's, GFNs, GUs, GMs, EMs, All of them have factors P, with P-1 known to have 20-25 bits already factored. You get this 20-25 bit boost for free and on top of it you get an additional factor of P-1, and as a result you get a factor P which is above what you can get with TF/sieving.
Prime95 tutorial say this

Quote:
 Pminus1=k,b,n,c,B1,B2[,"comma-separated-list-of-known-factors"]
Since I work on sequence 4*53^n+1 , and that is GFN seqeunce, I ask you where to find ( how to use, how setup) list-of-known-factors in Pminus1 line in Prime95 worktodo.txt

If 4*53^n+1 is NOT GFN sequences, then give me example of one GFN sequences in "CRUS world" :) so I can teach on that sequence.

If I undestand correctly if I know "list of know factors" , I will drasticaly increase chance to find factor.

Please give me clear examples, and thanks for answer this question (even it is maybe) useless or even stupid :)

P.S Since B1 and B2 gives me time of process for one test, I can adjust time per test. So dont bother with fact is P-1 efficient or it is not: I try to find, to learn, how to get for GFN sequences working process.
Will I lost 10 days and find few factors is irrelevant: if I learn ( with your help)

Thanks once more

Last fiddled with by pepi37 on 2017-07-30 at 13:47

2017-07-30, 15:30   #2
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

5×1,877 Posts

To quote from http://mathworld.wolfram.com/General...matNumber.html
Quote:
 There are two different definitions of generalized Fermat numbers, one of which is more general than the other.
This could be recursively repeated, if you want: There are two different definitions of the first kind of generalized Fermat numbers (a2^n + 1), one of which is more general than the other. One of them that a is a small number (less than 25 bits, so that if could be used as the basis for the virtual numeric system in which in turn the conventional FFT construction will be performed, and only then the calculations are fast) and n is >> 1. The second is that a can be anything and n is >=1, for example 1.

Chris Caldwell used "Generalized Fermat Number" in the first sense but in the second sub-kind. So when UTM database will mark for 4*53^n+1 with even n as a "Generalized Fermat Number", this only means that your numbers are of A^2^m+1 type where A is a very large number and m=1. The consequence of that these numbers will only have factors of type 4*t+1. P-1 will be not very useful or fast, but you can run it as written by you. It depends on what you actually want to do. If you want to run P-1 for the sake of just running P-1, you can. You will even find some factors.

Unsure about your confusion about what "comma-separated-list-of-known-factors" means. It means exactly that. Because we can assume that you are not in the business of "completely factoring of e.g. 53^1026*4+1" but that you are using P-1 for cleaning up your sieve file, then "comma-separated-list-of-known-factors" is an empty field, because you don't know any factors.
__________

What you quoted uses GFN in first sense and first sub-kind. n must be large for the P-1 to work effectively.

 2017-07-31, 15:03 #3 pepi37     Dec 2011 After milion nines:) 2×709 Posts As always thanks Batalov for answer Respect! So for me: puzzle is completed :) Continuing to search my big prime :) Last fiddled with by pepi37 on 2017-07-31 at 15:06

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