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: (58556121-1)/5854 Verification status (*): PRP Official Comment: Generalized repunit Unofficial Comments: This prime has 1 user comment below. Proof-code(s): (*): CH1 : Soule, Minovic, CHG, Primo, OpenPFGW Decimal Digits: 23058   (log10 is 23057.2646985606) Rank (*): 34292 (digit rank is 1) Entrance Rank (*): 20521 Currently on list? (*): short Submitted: 11/30/2005 08:42:21 CDT Last modified: 11/30/2005 08:59:11 CDT Database id: 76332 Status Flags: Verify Score (*): 35.0262 (normalized score 0.0037)

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 6
Subcategory: "Generalized Repunit"
(archival tag id 192030, 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.

David Broadhurst writes (30 Nov 2005): 

Validation of the CHG part of this proof was provided by chgcertd.gp (Version 0.6) included in http://physics.open.ac.uk/~dbroadhu/cert/n5855cert.zip and was completed in 12 seconds.

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 76332 person_id 9 machine Linux P4 2.8GHz what prp notes Command: /home/caldwell/client/pfgw -f -tc -q"(5855^6121-1)/5854" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing (5855^6121-1)/5854 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 7073109 Running N-1 test using base 17 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(10240,21) to FFT(10240,20) Reduced from FFT(10240,20) to FFT(10240,19) Reduced from FFT(10240,19) to FFT(10240,18) Reduced from FFT(10240,18) to FFT(10240,17) Reduced from FFT(10240,17) to FFT(10240,16) 153198 bit request FFT size=(10240,16) Running N-1 test using base 29 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(10240,21) to FFT(10240,20) Reduced from FFT(10240,20) to FFT(10240,19) Reduced from FFT(10240,19) to FFT(10240,18) Reduced from FFT(10240,18) to FFT(10240,17) Reduced from FFT(10240,17) to FFT(10240,16) 153198 bit request FFT size=(10240,16) Running N+1 test using discriminant 47, base 8+sqrt(47) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(10240,21) to FFT(10240,20) Reduced from FFT(10240,20) to FFT(10240,19) Reduced from FFT(10240,19) to FFT(10240,18) Reduced from FFT(10240,18) to FFT(10240,17) Reduced from FFT(10240,17) to FFT(10240,16) 153206 bit request FFT size=(10240,16) Calling N-1 BLS with factored part 1.01% and helper 0.03% (3.05% proof) (5855^6121-1)/5854 is Fermat and Lucas PRP! (365.1900s+0.0000s) [Elapsed time: 371 seconds] modified 2005-12-10 11:09:15 created 2005-11-30 08:53:00 id 81538