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: 2519951928 · 2459#+1 Verification status (*): Proven Official Comment: Cunningham chain 2nd kind (8p-7) Proof-code(s): (*): p155 : DavisK, NewPGen, OpenPFGW Decimal Digits: 1057   (log10 is 1056.1223197473) Rank (*): 81979 (digit rank is 55) Entrance Rank (*): 77653 Currently on list? (*): short Submitted: 2/1/2009 05:19:28 CDT Last modified: 2/1/2009 05:44:56 CDT Database id: 86482 Status Flags: none Score (*): 25.4428 (normalized score 0)

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.

Cunningham Chains (2nd kind) (archivable class *)

Prime on list: yes, rank 5, weight 39.3245444023371
Subcategory: "Cunningham chain 2nd kind (8p-7)"
(archival tag id 186991, tag last modified 2009-02-01 05:32:05)

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 86482 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/pfgw -t -q"2519951928*2459#+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 2519951928*2459#+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2467 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(448,22) to FFT(448,21) Reduced from FFT(448,21) to FFT(448,20) Reduced from FFT(448,20) to FFT(448,19) Reduced from FFT(448,19) to FFT(448,18) Reduced from FFT(448,18) to FFT(448,17) Reduced from FFT(448,17) to FFT(448,16) 7026 bit request FFT size=(448,16) Calling Brillhart-Lehmer-Selfridge with factored part 33.58% 2519951928*2459#+1 is prime! (0.4400s+0.0000s) [Elapsed time: 1.00 seconds] modified 2009-02-05 12:51:34 created 2009-02-01 05:23:01 id 102387

field value prime_id 86482 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/TrialDiv/TrialDiv -q 2519951928 2459 # 1 2>&1 [Ellapsed time: 149.280 seconds] modified 2009-02-01 05:44:56 created 2009-02-01 05:42:26 id 102395