20190522, 22:32  #12  
Dec 2011
New York, U.S.A.
97 Posts 
Quote:
Then we looked in the LLR source code. It's not there. 

20190523, 05:41  #13 
Jun 2007
Seattle, WA
5 Posts 
That flag does not work w/ the 3.8.23 release of LLR.

20190708, 13:39  #14 
Einyen
Dec 2003
Denmark
2^{2}×733 Posts 

20190920, 06:56  #15 
May 2015
3 Posts 
What happens if LLR cannot factorize 'b' ? It may happen with big GFN numbers, having very high 'b'. Probably aprcl.exe should help with factorization, but we don't include it in Boinc setups. Without aprcl, internal factorization fails and a warning is printed:
>cllr64.3.8.23.exe d q"1814570322897374^65536+1" Error 2 while trying to create new process Error 2 while trying to create new process Base factorized as : 2*7*67*1934509939123*1 Base cofactor : 1934509939123, 1 (Must be proven prime or factorized externally) In the example above, 1934509939123 is prime. But what happens in theoretical case if LLR accepts composite cofactor? Will the prime test itself work correctly? 
20200519, 02:37  #16 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{2}×2,281 Posts 
I am posting a patch to LLR that allows to run the "Proth.exe" like test for k*b^n+1 dividing some large cyclotomic Phi(b^m,2).
The input file should have the following magic header: Code:
ABC DivPhi($a*$b^$c+1) 2 3 822 2 3 897 2 3 1252 2 3 1454 2 3 4217 Code:
2*3^822+1 does not divide 2^3^8221 Time : 263.342 ms. 2*3^897+1 Divides 2^3^8971 Time : 116.718 ms. 2*3^897+1 Divides 2^3^8961 Time : 103.216 ms. 2*3^897+1 does not divide 2^3^8951 Time : 101.769 ms. Conclusion: 2*3^897+1 Divides Phi(3^896,2) 2*3^1252+1 does not divide 2^3^12521 Time : 97.786 ms. 2*3^1454+1 does not divide 2^3^14541 Time : 109.374 ms. 2*3^4217+1 Divides 2^3^42171 Time : 37.989 ms. 2*3^4217+1 does not divide 2^3^42161 Time : 50.651 ms. Conclusion: 2*3^4217+1 Divides Phi(3^4217,2) 
20200521, 13:53  #17  
May 2004
FRANCE
2^{4}·5·7 Posts 
Thank you Serge!
Quote:
I hope you are well and take care of you by these times... Best Regards, Jean 

20200521, 16:06  #18 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{2}×2,281 Posts 
Thank you Jean!
This code is 56 years old so it passed a lot of internal testing (though this time I restored it from memory from scratch and of course, with modern LLR, one can now use m/t). I have extensively used it previously and I have already tested all known "Divides Phi numbers" (not just visible top 20; all such numbers including tiny ones can be found by UTM search, using option "all"). All past Proth.exebased results are reproduced. There are additional checks that I can provide later  so that we can quit this test very early; if by Euler's criterion we can immediately check that 2^b^n1 will not be zero without computation. 
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