20221205, 10:56  #1 
Sep 2022
Netherlands
5 Posts 
Different results in llr2 1.3.0
We were testing for PRPs in the form 6^$a+$a and found conflicting results between LLR2 1.3.0 and other versions.
In LLR2 1.1.0 the sum 6^85481+85481 is found to be PRP: Code:
.\llr2_1.1.0_win64_201114.exe d q"6^85481+85481" Starting probable prime test of 6^85481+85481 Using zeropadded FMA3 FFT length 24K, Pass1=384, Pass2=64, clm=2, a = 3 6^85481+85481 is base 3Fermat PRP! (66518 decimal digits) Time : 10.909 sec. Starting Lucas sequence Using zeropadded FMA3 FFT length 24K, Pass1=384, Pass2=64, clm=2, P = 5, Q = 3 6^85481+85481 is Fermat and Lucas PRP, Starting Frobenius test sequence Using zeropadded FMA3 FFT length 24K, Pass1=384, Pass2=64, clm=2, Q = 3 6^85481+85481 is Fermat, Lucas and Frobenius PRP! (P = 5, Q = 3, D = 13) Time : 56.028 sec. Code:
pfgw_win_4.0.3\distribution> .\pfgw64.exe q"6^85481+85481" PFGW Version 4.0.3.64BIT.20220704.Win_Dev [GWNUM 29.8] 6^85481+85481 is 3PRP! (11.1294s+0.0009s) Code:
llr21.3.0win64> .\llr2.exe d q"6^85481+85481" Starting probable prime test of 6^85481+85481 Using zeropadded FMA3 FFT length 24K, Pass1=384, Pass2=64, clm=2, a = 3 6^85481+85481 is not prime. RES64: BA67AB5CB68EFF1B. OLD64: 2F37021623ACFD4E Time : 10.505 sec. Last fiddled with by MischaR on 20221205 at 10:57 
20221205, 11:00  #2 
Sep 2021
Canada
2 Posts 
Yeah, I can personally confirm this, being the one to initially get a conflicting result after I attempted to run a confirmatory test on the PRP 6^85,481 + 85,481. It confused me greatly.
Last fiddled with by ikari on 20221205 at 11:14 Reason: Mistakenly identified MischaR as the finder of the PRP, when it was actually found in 2014 
20221205, 12:33  #3  
May 2004
FRANCE
3×5×41 Posts 
Correct results using LLR 4.0.3
Quote:
jpenne@crazycomp:~/Chance$ llr64 d q"6^85481+85481" Starting probable prime test of 6^85481+85481 Using zeropadded FMA3 FFT length 24K, Pass1=384, Pass2=64, clm=2, a = 3 6^85481+85481 is base 3Fermat PRP! (66518 decimal digits) Time : 23.654 sec. Starting Lucas sequence Using zeropadded FMA3 FFT length 25K, Pass1=320, Pass2=80, clm=2, P = 5, Q = 3 6^85481+85481 is Fermat and Lucas PRP, Starting Frobenius test sequence Using zeropadded FMA3 FFT length 25K, Pass1=320, Pass2=80, clm=2, Q = 3 6^85481+85481 is Fermat, Lucas and Frobenius PRP! (P = 5, Q = 3, D = 13) Time : 110.724 sec. jpenne@crazycomp:~/Chance$ llr64 oBPSW=1 d q"6^85481+85481" Starting probable prime test of 6^85481+85481 Using zeropadded FMA3 FFT length 24K, Pass1=384, Pass2=64, clm=2, a = 2 6^85481+85481 is base 2Fermat PRP! (66518 decimal digits) Time : 25.134 sec. Starting Lucas sequence Using zeropadded FMA3 FFT length 25K, Pass1=320, Pass2=80, clm=2, P = 1, Q = 2 6^85481+85481 is Fermat and BPSW PRP, Starting Frobenius test sequence Using zeropadded FMA3 FFT length 25K, Pass1=320, Pass2=80, clm=2, Q = 2 6^85481+85481 is Fermat, BPSW and Frobenius PRP! (P = 1, Q = 2, D = 7) Time : 108.835 sec. Regards, Jean 

20221205, 13:05  #4 
"Jeppe"
Jan 2016
Denmark
184_{10} Posts 
For what it is worth, PARI/GP's function ispseudoprime(6^85481+85481) returns 1 (i.e. this is a probable prime). I believe its implementation is independent of gwnum? It does a test that is more thorough than just a 3PRP test.
Also, this PRP was reported in 2014 by Henri Lifchitz: 6^85481+85481 /JeppeSN 
20221205, 18:41  #5  
Einyen
Dec 2003
Denmark
110101101010_{2} Posts 
Quote:
But if you meant it as a "bug report", I think you posted it in the wrong place. There are no LLR2 development threads/forums here it seems, LLR2 seems to come from here: https://github.com/patnashev/llr2 

20221205, 19:27  #6 
"Mark"
Apr 2003
Between here and the
2×59^{2} Posts 
AFAIK, llr2 does not do a PRP test. llr2 cannot do a primality test on this number. So it might be PRP, but llr2 can't tell you because it didn't do a PRP test.
If I am wrong about llr2 regarding its ability to do a PRP test, then please let us know. 
20221205, 19:38  #7 
Sep 2011
Germany
2^{3}×7×61 Posts 
An older version of llr2 with gwnum 29.8 is correct, there is a bug in the gwnum 30.9 in the latest llr2 app and was reported today from the primegrid dev, k*b^n+/1 should not be affected.

20221206, 17:36  #8 
Sep 2011
Germany
2^{3}·7·61 Posts 
Another sample for Riesel / Sieve:
input 175000000000:P:1:51:257 607920 35218 llr2.exe gwnum 30.9 11920*51^35219+1 is not prime. RES64: 5326FBF23EE99827 Time : 12.728 sec. llr3.8.21 607920*51^35218+1 is not prime. RES64: 5326FBF23EE99827. OLD64: 8C5E80CE11E6EA41 Time : 26.106 sec. llr2 gwnum 30.4 11920*51^35219+1 is not prime. RES64: 5326FBF23EE99827 Time : 38.737 sec. llr2 gwnum 29.8 607920*51^35218+1 is not prime. RES64: 5326FBF23EE99827 Time : 51.552 sec. The app converts the number 607920 / 51 = 11920 @George: only gwnum 30.x is affected 
20221207, 09:38  #9  
"Jeppe"
Jan 2016
Denmark
270_{8} Posts 
Quote:


20221207, 14:00  #10  
Sep 2011
Germany
D58_{16} Posts 
Quote:


20221207, 19:04  #11 
"Alexander"
Nov 2008
The Alamo City
1631_{8} Posts 
This isn't an issue with the latest version of "regular" LLR (4.0.3), with gwnum 30.6:
Code:
607920*51^35218+1 is not prime. RES64: 5326FBF23EE99827. OLD64: 8C5E80CE11E6EA41 Time : 21.168 sec. Last fiddled with by Happy5214 on 20221207 at 19:05 
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