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: 229727 + 20273 Verification status (*): PRP Official Comment: ECPP Unofficial Comments: This prime has 1 user comment below. Proof-code(s): (*): c18 : Luhn, Primo Decimal Digits: 8949   (log10 is 8948.7186811032) Rank (*): 64973 (digit rank is 1) Entrance Rank (*): 43814 Currently on list? (*): no Submitted: 7/28/2009 22:47:16 CDT Last modified: 7/28/2009 23:20:22 CDT Database id: 89447 Status Flags: Verify Score (*): 32.0957 (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.

Elliptic Curve Primality Proof (archivable *)

Prime on list: no, rank 58
Subcategory: "ECPP"
(archival tag id 210480, tag last modified 2013-06-16 10:20:28)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

David Broadhurst writes (29 Jul 2009): 

certificate

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 89447 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 1 2 29727 20273 2>&1 [Elapsed time: 8.526 seconds] modified 2011-12-27 16:48:43 created 2009-07-28 22:48:01 id 108262

field value prime_id 89447 person_id 9 machine RedHat P4 P4 what prp notes Command: /home/caldwell/client/pfgw -tc -q"2^29727+20273" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 2^29727+20273 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 11 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(3584,21) to FFT(3584,20) Reduced from FFT(3584,20) to FFT(3584,19) Reduced from FFT(3584,19) to FFT(3584,18) Reduced from FFT(3584,18) to FFT(3584,17) 59464 bit request FFT size=(3584,17) Running N+1 test using discriminant 19, base 9+sqrt(19) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(3584,21) to FFT(3584,20) Reduced from FFT(3584,20) to FFT(3584,19) Reduced from FFT(3584,19) to FFT(3584,18) Reduced from FFT(3584,18) to FFT(3584,17) 59472 bit request FFT size=(3584,17) Calling N+1 BLS with factored part 0.08% and helper 0.07% (0.30% proof) 2^29727+20273 is Fermat and Lucas PRP! (45.4350s+0.1018s) [Elapsed time: 46.00 seconds] modified 2009-08-11 11:44:22 created 2009-07-28 22:53:01 id 108263