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: 787302705 · 256790+1 Verification status (*): Proven Official Comment: Cunningham chain 2nd kind (2p-1) Proof-code(s): (*): g336 : Tornberg, PRP, NewPGen, Proth.exe Decimal Digits: 17105   (log10 is 17104.3895955) Rank (*): 37561 (digit rank is 2) Entrance Rank (*): 21318 Currently on list? (*): no Submitted: 3/13/2005 14:14:36 CDT Last modified: 3/13/2005 14:14:36 CDT Database id: 73724 Status Flags: none Score (*): 34.1024 (normalized score 0.0014)

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: no, rank 6, weight 33.8245659882852
Subcategory: "Cunningham chain 2nd kind (2p-1)"
(archival tag id 192400, tag last modified 2009-11-08 00:20:25)

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 73724 person_id 9 machine Linux P4 2.8GHz what prime notes Command: /home/caldwell/client/pfgw -f -t -q"787302705*2^56790+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 787302705*2^56790+1 [N-1, Brillhart-Lehmer-Selfridge] trial factoring to 5128198 Running N-1 test using base 13 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(7168,21) to FFT(7168,20) Reduced from FFT(7168,20) to FFT(7168,19) Reduced from FFT(7168,19) to FFT(7168,18) Reduced from FFT(7168,18) to FFT(7168,17) Reduced from FFT(7168,17) to FFT(7168,16) 113648 bit request FFT size=(7168,16) Calling Brillhart-Lehmer-Selfridge with factored part 99.95% 787302705*2^56790+1 is prime! (42.8161s+0.0003s) modified 2005-03-29 11:22:33 created 2005-03-13 14:23:41 id 78739