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: 45 · 2458712+1 Verification status (*): Proven Official Comment: Divides GF(458709,5), GF(458710,6) [K] Proof-code(s): (*): L170 : Crosa, LLR Decimal Digits: 138088   (log10 is 138087.72458353) Rank (*): 5544 (digit rank is 1) Entrance Rank (*): 1134 Currently on list? (*): short Submitted: 6/3/2007 06:02:33 CDT Last modified: 9/18/2007 22:20:02 CDT Database id: 80865 Status Flags: none Score (*): 40.5482 (normalized score 0.9342)

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 18, weight 44.3549046604655
Subcategory: "Divides GF(*,6)"
(archival tag id 187436, tag last modified 2009-06-21 13:20:19)

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

Prime on list: no, rank 21, weight 44.3549046604655
Subcategory: "Divides GF(*,5)"
(archival tag id 187435, tag last modified 2009-08-25 17:20:41)

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 80865 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 45 2 458712 1 2>&1 [Elapsed time: 9.895 seconds] modified 2007-09-12 06:50:19 created 2007-06-03 06:22:01 id 90841

field value prime_id 80865 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/pfgw -t -q"45*2^458712+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 45*2^458712+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 13 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(57344,20) to FFT(57344,19) Reduced from FFT(57344,19) to FFT(57344,18) Reduced from FFT(57344,18) to FFT(57344,17) 917444 bit request FFT size=(57344,17) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 45*2^458712+1 is prime! (1115.8100s+0.0000s) [Elapsed time: 1117 seconds] modified 2007-09-12 06:50:19 created 2007-06-03 06:23:01 id 90842