7 · 23511774 + 1

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important PrimePages database: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes.

Description:7 · 23511774 + 1
Verification status (*):Proven
Official Comment (*):Divides GF(3511773,6)
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p236 : Cooper, NewPGen, PRP, OpenPFGW
Decimal Digits:1057151   (log10 is 1057150.15709092)
Rank (*):387 (digit rank is 1)
Entrance Rank (*):21
Currently on list? (*):short
Submitted:11/14/2008 15:17:50 CDT
Last modified:11/24/2008 21:50:02 CDT
Database id:85758
Status Flags:none
Score (*):46.8035 (normalized score 12.9947)

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 4, weight 48.7494651442748
Subcategory: "Divides GF(*,6)"
(archival tag id 187014, tag last modified 2020-03-08 07:50:14)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

Curtis Cooper writes (11 Sep 2014):  (report abuse)
7*2^3511774+1 is a Factor of GF(3511773,6)
7*2^3511774+1 is a Factor of GF(3511770,7)
7*2^3511774+1 is a Factor of xGF(3511773,7,6)
7*2^3511774+1 is a Factor of xGF(3511771,10,9)
7*2^3511774+1 is a Factor of xGF(3511771,11,2)
7*2^3511774+1 is a Factor of xGF(3511773,12,11)

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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 7 2 3511774 1 2>&1 [Elapsed time: 11.255 seconds]
modified2020-07-07 17:30:39
created2008-11-14 15:22:01

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -t -q"7*2^3511774+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 7*2^3511774+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(458752,19) to FFT(458752,18) Reduced from FFT(458752,18) to FFT(458752,17) Reduced from FFT(458752,17) to FFT(458752,16) 7023562 bit request FFT size=(458752,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 7*2^3511774+1 is prime! (103531.8685s+0.0026s) [Elapsed time: 28.76 hours]
modified2020-07-07 17:30:39
created2008-11-14 15:23:01

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.
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