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: 2132049-1 Verification status (*): Proven Official Comment: Mersenne 30 Proof-code(s): (*): S : Slowinski Decimal Digits: 39751   (log10 is 39750.7098974331) Rank (*): 26747 (digit rank is 1) Entrance Rank (*): 1 Currently on list? (*): short Submitted: 9/20/1983 Last modified: 9/20/1983 Database id: 2220 Status Flags: none Score (*): 36.7089 (normalized score 0.02)

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.

Mersenne (archivable *)

Prime on list: yes, rank 18
Subcategory: "Mersenne"
(archival tag id 190675, tag last modified 2009-06-13 12:41:00)

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 2220 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/pfgw -tp -q"2^132049-1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 2^132049-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 3, base 1+sqrt(3) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(16384,20) to FFT(16384,19) Reduced from FFT(16384,19) to FFT(16384,18) Reduced from FFT(16384,18) to FFT(16384,17) 264114 bit request FFT size=(16384,17) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 2^132049-1 is prime! (203.5100s+0.0000s) [Elapsed time: 3.38 minutes] modified 2008-09-12 14:12:35 created 2008-08-05 20:48:11 id 100209

field value prime_id 2220 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/llr.pl 1*2^132049-1 2>&1 Prime95 or Mprime are much better to test this Mersenne number !! Starting Lucas-Lehmer loop... 1*2^132049-1 is prime! Time : 23.743 sec. [Elapsed time: 24.00 seconds] modified 2008-09-12 14:12:35 created 2008-08-06 19:14:32 id 100218