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Old 2016-08-29, 18:57   #1
wombatman
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Default Double-Check

Could someone double-check the primality of 63998*297^21888-1?

It passes 3, 5, 7, and 11 Fermat PRP but fails the N+1 BLS test via PFGW. I'd appreciate someone else confirming one way or the other.
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Old 2016-08-29, 19:15   #2
Batalov
 
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Phi(4,2^7658614+1)/2

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It is prime.
Code:
Using zero-padded FMA3 FFT length 28K, Pass1=448, Pass2=64, a = 3
...
Using zero-padded FMA3 FFT length 30K, Pass1=384, Pass2=80, a = 3
...
U((N+1)/11) is coprime to N!
U((N+1)/3) is coprime to N!
63998*297^21888-1 is prime! (54129 decimal digits, P = 3)  Time : 56.775 sec.
Try -a1 -a2 (etc) options.
Also, try LLR (and optionally, add FFT_Increment=1 (or 2, or 3) to llr.ini
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Old 2016-08-29, 20:25   #3
lalera
 
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./sllr64 -q63998*297^21888-1
63998*297^21888-1 is prime! (54129 decimal digits, P = 3) Time : 198.176 sec.
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Old 2016-08-29, 20:46   #4
wombatman
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Thanks to both of you. For full clarification, here's what I get with PFGW's "-tp" switch:

Code:
$ pfgw64.exe -f0 -a1 -tp -q"63998*297^21888-1"
PFGW Version 3.7.10.64BIT.20150809.Win_Dev [GWNUM 28.6]

No factoring at all, not even trivial division
Primality testing 63998*297^21888-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 2, base 2+sqrt(2)
63998*297^21888-1 is composite (240.1252s+0.0018s)
I went ahead and used LLR to confirm that it's prime.

Last fiddled with by wombatman on 2016-08-29 at 20:47
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