7 · 22139912 + 1

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Description: 7 · 22139912 + 1 Proven Divides GF(2139911,12) This prime has 1 user comment below. g279 : Cooper, NewPGen, PRP, Proth.exe 644179   (log10 is 644178.54517934) 1871 (digit rank is 1) 34 short 5/12/2007 15:05:08 CDT 8/22/2007 22:50:03 CDT 80448 none 45.2832 (normalized score 2.8352)

Archival tags:

There are certain forms classed as archivable: these prime may (at times) remain on this list even if they do not make the Top 5000 proper.  Such primes are tracked with archival tags.
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 9, weight 47.2291304267237
Subcategory: "Divides GF(*,12)"
(archival tag id 187039, tag last modified 2020-06-04 18:20:04)

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Curtis Cooper writes (11 Sep 2014):  (report abuse)
 7*2^2139912+1 is a Factor of xGF(2139911,5,2) 7*2^2139912+1 is a Factor of xGF(2139908,7,4) 7*2^2139912+1 is a Factor of xGF(2139910,9,8) 7*2^2139912+1 is a Factor of xGF(2139911,10,7) 7*2^2139912+1 is a Factor of xGF(2139910,11,3) 7*2^2139912+1 is a Factor of GF(2139911,12)

Verification data:

The Top 5000 Primes is a list for proven primes only. In order to maintain the integrity of this list, we seek to verify the primality of all submissions.  We are currently unable to check all proofs (ECPP, KP, ...), but we will at least trial divide and PRP check every entry before it is included in the list.
fieldvalue
prime_id80448
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"7*2^2139912+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 7*2^2139912+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(262144,19) to FFT(262144,18) Reduced from FFT(262144,18) to FFT(262144,17) 4279838 bit request FFT size=(262144,17) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 7*2^2139912+1 is prime! (-2041.6784s+0.0000s) [Elapsed time: 33487 seconds]
modified2020-07-07 17:30:41
created2007-05-12 15:10:15
id89991

fieldvalue
prime_id80448
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 7 2 2139912 1 2>&1 [Elapsed time: 10.434 seconds]
modified2020-07-07 17:30:41
created2007-05-12 15:22:01
id89992

Query times: 0.0007 seconds to select prime, 0.0002 seconds to seek comments.