20141215, 07:56  #1 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
23513_{8} Posts 
A possible bug in LLR/PFGW while using GWNUM (no bug in P95)
Hmmm...
I added PRPBase=7 to prime.txt and I got that 1024 · 3^1877301 + 1 is a 7PRP (??). I changed PRPBase=11 in prime.txt and I got that 1024 · 3^1877301 + 1 is a 11PRP (??). Yet it is a composite by pfgw and llr (or mprime doesn't actually change the base). Though it is likely a 3PRP (and a 3SPRP by llr). I am using one worker with 12, 16, 24 threads (27.9, the AVX code is being used). Maybe the multithreaded code doesn't change the base? 
20141215, 08:10  #2 
Jun 2003
2×2,719 Posts 

20141215, 08:44  #3 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
3·7·479 Posts 
That's a good idea! Thanks. RES64 values are different!
I've now put PRPBase=5 everywhere. Before [PrimeNet] section, after, and in local.txt, too. ;) Now, I am thinking, maybe this is after all a prime? Can't be so easily a 7PRP and a 11PRP and a 3PRP and then a composite. Maybe the reason is a devious FFT overflow. 
20141215, 09:04  #4 
Jun 2003
2×2,719 Posts 

20141215, 09:20  #5 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
3·7·479 Posts 
Yes, I am running that but it will take quite a bit of time.
Another one that I am running (actually times five): llr N1 with FermatBase=7, 11, 13, 17, 19 (you change it in llr.ini, before the test). What is nice is that with a=11, a different FFT size is chosen. (For a=5 240K, for a=11, 256K.) 
20141215, 10:08  #6 
Jun 2003
1010100111110_{2} Posts 
FWIW
Code:
1024*3^1877301+1 is a probable prime! We4: EC696ADA,00000000 Code:
PRPBase=2 
20141215, 11:23  #7 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
3×7×479 Posts 
My pfgw runs finished. By them, ... it is a prime, after all.
Code:
PFGW Version 3.7.2.64BIT.20130122.x86_Dev [GWNUM 27.9] Output logging to file pfgw.out Factoring numbers to 1% of normal. Primality testing 1024*3^1877301+1 [N1, BrillhartLehmerSelfridge] Running N1 test using base 5 1024*3^1877301+1 is prime! (12398.0381s+0.0164s) (Plus many PRP tests in many bases with P95 are positive. The a2 test is still running...) 
20141215, 11:50  #8  
Jun 2003
2×2,719 Posts 
Quote:
I think in all such cases, we should suspect the proof test, because it is much more probable that an error caused the "composite" result rather than the incredibly rare occurrence of a large pseudoprime. 

20141215, 11:59  #9 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
3·7·479 Posts 
This is probably confined to k*b^n+1 where b>2, especially b=3 (because the default PRP/N1 test base is 3). Only those who hunt for "nonboring" primes occasionally step into these traps  this includes people at CRUS.
b=2 is relatively much better debugged  traditional Proth/Riesel which are the mainstream. The prime database is cracking at the seams with these (esp. the b=2, n=1290000). 
20141215, 22:01  #10 
Sep 2002
Database er0rr
5·29·31 Posts 
How many digits does your problem number have? I ask because TPP says 895704, but I get this:
Code:
./pfgw64 od q"1024*3^1877301+1" PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] 1024*3^1877301+1: 16554132 <SNIP> 818435073 Code:
wc Serge 1 1 895705 Serge Last fiddled with by paulunderwood on 20141215 at 22:08 
20141215, 22:13  #11 
P90 years forever!
Aug 2002
Yeehaw, FL
8164_{10} Posts 
I ran this using prime95 version 28.5 with AVX but not FMA FFTs. Prime95 chose a 240K FFT size. Round off error was only 0.02. It worked.
My conclusion is the problem is not in choosing an FFT size that is too small. Either a GWNUM bug was fixed between 27.9 and 28.5 or PFGW's PRP code is doing something subtly different than prime95's and either has a bug or reveals a bug in GWNUM. I'm a little confused about what is failing in PFGW. Does PFGW report it as a PRP or is the problem only in the N1 proving code? 
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