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: (142614663-1)/14260 Verification status (*): PRP Official Comment: Generalized repunit Unofficial Comments: This prime has 1 user comment below. Proof-code(s): (*): c13 : Steward, OpenPFGW, Primo Decimal Digits: 19367   (log10 is 19366.647236662) Rank (*): 36101 (digit rank is 1) Entrance Rank (*): 28438 Currently on list? (*): short Submitted: 11/4/2007 13:44:21 CDT Last modified: 11/4/2007 14:01:12 CDT Database id: 82859 Status Flags: Verify Score (*): 34.4867 (normalized score 0.0021)

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.

Generalized Repunit (archivable *)

Prime on list: yes, rank 8
Subcategory: "Generalized Repunit"
(archival tag id 192271, tag last modified 2009-07-12 03:50:27)

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.

Andrew A. D. Steward writes (4 Nov 2007): 

Certificate at http://www.primes.viner-steward.org/andy/E/37B51237.html

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 82859 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/pfgw -o -f -q"(14261^4663-1)/14260" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 5862403 (14261^4663-1)/14260 has no small factor. [Ellapsed time: 9.740 seconds] modified 2008-01-03 10:54:43 created 2007-11-04 13:52:17 id 94834

field value prime_id 82859 person_id 9 machine RedHat P4 P4 what prp notes Command: /home/caldwell/client/pfgw -tc -q"(14261^4663-1)/14260" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing (14261^4663-1)/14260 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 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) 128678 bit request FFT size=(7168,18) Running N-1 test using base 3 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) 128678 bit request FFT size=(7168,18) 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(7168,21) to FFT(7168,20) Reduced from FFT(7168,20) to FFT(7168,19) Reduced from FFT(7168,19) to FFT(7168,18) 128686 bit request FFT size=(7168,18) Calling N-1 BLS with factored part 0.78% and helper 0.00% (2.34% proof) (14261^4663-1)/14260 is Fermat and Lucas PRP! (203.2000s+0.0000s) [Elapsed time: 3.43 minutes] modified 2008-01-03 10:54:43 created 2007-11-04 13:57:46 id 94837