37674760044125 · 2^1513679 - 67931

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Lei Zhou writes (11 Sep 2014):  (report abuse)

This prime is proven using id=82770 prime as helper. It can be written as 67930*((33305**2^756839)^2-1)-1, which is canonicalized to the listed form. The helper was proven prime using LLR on 2007-10-28 09:52:12. Then the current prime is proven using OpenPFGW with id=82770 as helper. Certificate shown below: ./pfgw -tc -l"33965.proof" -h"helper" -q"2*33965*(33305*33305*2^1513678-1)-1" Primality testing 2*33965*(33305*33305*2^1513678-1)-1 [N-1/N+1, Brillhart-Lehmer-Selfridge] Primality testing 2*33965*(33305*33305*2^1513678-1)-1 [N-1/N+1, Brillhart-Lehmer-Selfridge] Primality testing 2*33965*(33305*33305*2^1513678-1)-1 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Primality testing 2*33965*(33305*33305*2^1513678-1)-1 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 11, base 1+sqrt(11) Running N+1 test using discriminant 11, base 3+sqrt(11) Calling N+1 BLS with factored part 50.00% and helper 0.00% (150.01% proof) 2*33965*(33305*33305*2^1513678-1)-1 is prime! (145794.4785s+0.0615s)

Verification data:

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