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 · 2368554-405769059 · 2180009-1 Verification status (*): Proven Official Comment: Arithmetic progression (3,d=45*2^368553-405769059*2^180009) Proof-code(s): (*): p108 : Sun, OpenPFGW Decimal Digits: 110948   (log10 is 110947.462234457) Rank (*): 8713 (digit rank is 1) Entrance Rank (*): 258 Currently on list? (*): short Submitted: 12/10/2003 00:10:52 CDT Last modified: 12/10/2003 00:10:52 CDT Database id: 67622 Status Flags: none Score (*): 39.8743 (normalized score 0.4759)

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.

Arithmetic Progressions of Primes (archivable class *)

Prime on list: yes, rank 3, weight 46.6539543178081
Subcategory: "Arithmetic progression (3,d=*)"
(archival tag id 187579, tag last modified 2009-02-12 20:20:07)

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 67622 person_id 9 machine Linux P4 2.8GHz what prime notes Command: /home/caldwell/client/pfgw -f -tp -q"45*2^368554-405769059*2^180009-1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 45*2^368554-405769059*2^180009-1 [N+1, Brillhart-Lehmer-Selfridge] trial factoring to 38087958 Running N+1 test using discriminant 7, base 1+sqrt(7) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(49152,20) to FFT(49152,19) Reduced from FFT(49152,19) to FFT(49152,18) Reduced from FFT(49152,18) to FFT(49152,17) Reduced from FFT(49152,17) to FFT(49152,16) 737136 bit request FFT size=(49152,16) Calling Brillhart-Lehmer-Selfridge with factored part 48.84% 45*2^368554-405769059*2^180009-1 is prime! (-1059.2446s+0.0000s) modified 2004-01-16 11:28:35 created 2003-12-10 00:23:00 id 72559