Thread: other conjectures View Single Post
2020-07-21, 03:23   #22
sweety439

Nov 2016

22·19·31 Posts

Quote:
 Originally Posted by gd_barnes Please change srsieve to remove the error check for divisibility by 2 and then force the regular sieve process to remove the terms divisible by 2 instead. Is that really difficult? It seems like a simple fix. I'm pretty sure I or others have requested this before and we seem to keep getting the run-around about it. To be more specific below is what Sweety and I and others want to do when attempting to test a conjecture such as (13*43^n-1)/2 if the form is not found to have a smallish prime using simple trial factoring with PFGW. 1. Sieve using srsieve using the form 13*43^n-1 but with a starting sieve depth of 3 using the following command: srsieve -G -p 3 -P 1e9 -n 25e3 -N 100e3 -m 1e9 "13*43^n-1" This tells srsieve to only sieve the form for P=3 to 1e9. That way it does not remove the terms that are divisible by 2 (which would be all of them in this case). 2. Test with PFGW using a standard PFGW header of: (ABC $a*43^$b-1)/2 // {number_primes,\$a,1} 13 25007 13 25019 (etc.) This allows us to both sieve and test the form (13*43^n-1)/2. Srsieve currently works for us if we have a form with a prime divisor other than 2 such as (13*46^n-1)/3. In that case we would just have it sieve the range of P=5 to 1e9 and there would be no error as there is in the case of (13*43^n-1)/2. Does this make sense? [ All of these are examples. They are not actual work done.] If this cannot be done please let us know and we will not request it anymore. We would prefer not to have to run a separate program when standard srsieve will work for 99% of cases like this. Also please let us know how you would sieve the form (13*43^n-1)/2. That would be very helpful.
The divisor of k*b^n+-1 (+ for Sierp, - for Riesel) is always gcd(k+-1,b-1) (+ for Sierp, - for Riesel) (see post https://mersenneforum.org/showpost.p...&postcount=230), since gcd(k+-1,b-1) is the trivial factor of k*b^n+-1, it is simply to take out this factor, thus, the divisor of R43, k=13 is 6, not 2 (gcd(13-1,43-1) = 6), and the formula of R43, k=13 is (13*43^n-1)/6, not (13*43^n-1)/2