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

This prime's information:

field (help) value Description: 7 · 22167800+1 Verification status (*): Proven Official Comment: Divides Fermat F(2167797), GF(2167799,5), GF(2167799,10) Unofficial Comments: This prime has 1 user comment below. Proof-code(s): (*): g279 : Cooper, PRP, NewPGen, Proth.exe Decimal Digits: 652574   (log10 is 652573.66969842) Rank (*): 60 (digit rank is 1) Entrance Rank (*): 30 Currently on list? (*): short Submitted: 4/15/2007 21:00:23 CDT Last modified: 4/23/2007 09:20:13 CDT Database id: 80047 Status Flags: none Score (*): 45.3229 (normalized score 110.6963)

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 1, weight 47.2688855381465
Subcategory: "Divides GF(*,10)"
(archival tag id 187032, tag last modified 2009-02-12 20:20:07)

Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)

Prime on list: yes, rank 3, weight 47.2688855381465
Subcategory: "Divides GF(*,5)"
(archival tag id 187031, tag last modified 2009-04-16 13:50:04)

Prime Fermat Divisors (archivable *)

Prime on list: yes, rank 2, weight 47.2688855381465
Subcategory: "Divides Fermat"
(archival tag id 187030, tag last modified 2009-02-12 20:20:07)

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 (19 Apr 2007): 

7*2^2167800+1 is a Factor of F2167797 7*2^2167800+1 is a Factor of GF(2167799,5) 7*2^2167800+1 is a Factor of xGF(2167799,5,2) 7*2^2167800+1 is a Factor of xGF(2167799,5,4) 7*2^2167800+1 is a Factor of GF(2167794,7) 7*2^2167800+1 is a Factor of xGF(2167797,7,2) 7*2^2167800+1 is a Factor of xGF(2167796,7,4) 7*2^2167800+1 is a Factor of xGF(2167799,7,5) 7*2^2167800+1 is a Factor of xGF(2167799,8,5) 7*2^2167800+1 is a Factor of xGF(2167797,8,7) 7*2^2167800+1 is a Factor of GF(2167799,10) 7*2^2167800+1 is a Factor of xGF(2167799,10,7)

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.

field value prime_id 80047 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 7 2 2167800 1 2>&1 [Elapsed time: 11.213 seconds] modified 2007-04-21 22:36:37 created 2007-04-15 21:22:01 id 89204

field value prime_id 80047 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/pfgw -t -q"7*2^2167800+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 7*2^2167800+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) 4335614 bit request FFT size=(262144,17) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 7*2^2167800+1 is prime! (-1504.0284s+0.0000s) [Elapsed time: 32885 seconds] modified 2007-04-21 22:36:37 created 2007-04-15 21:23:01 id 89205