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: 10127590 + 1042297 · (9 · 1042997 - 2)/11 + 1 Verification status (*): PRP Official Comment: Tetradic palindrome Unofficial Comments: This prime has 1 user comment below. Proof-code(s): (*): x40 : Bedwell, Broadhurst, OpenPFGW Decimal Digits: 127591   (log10 is 127590) Rank (*): 26085 (digit rank is 1) Entrance Rank (*): 5750 Currently on list? (*): no Submitted: 9/1/2009 17:34:33 CDT Last modified: 9/1/2009 19:20:22 CDT Database id: 89824 Status Flags: Verify Score (*): 40.3047 (normalized score 0.0816)

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.

Palindrome (archivable *)

Prime on list: no, rank 21
Subcategory: "Palindrome"
(archival tag id 210507, tag last modified 2013-01-08 06:50:30)

Tetradic (deprecated *)

Prime on list: no, rank 3
Subcategory: "Tetradic"
(archival tag id 210508, tag last modified 2009-09-08 14:50:32)

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 (1 Sep 2009): 

KP proof

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 89824 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/pfgw -o -f -q"10^127590+10^42297*(9*10^42997-2)/11+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 44215937 10^127590+10^42297*(9*10^42997-2)/11+1 has no small factor. [Elapsed time: 431.802 seconds] modified 2011-12-27 16:48:42 created 2009-09-01 17:35:02 id 109020

field value prime_id 89824 person_id 9 machine Ditto P4 P4 what prp notes Command: /home/ditto/client/pfgw -t -q"10^127590+10^42297*(9*10^42997-2)/11+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 10^127590+10^42297*(9*10^42997-2)/11+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(57344,20) to FFT(57344,19) Reduced from FFT(57344,19) to FFT(57344,18) Reduced from FFT(57344,18) to FFT(57344,17) Reduced from FFT(57344,17) to FFT(57344,16) 847698 bit request FFT size=(57344,16) Running N-1 test using base 13 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(57344,20) to FFT(57344,19) Reduced from FFT(57344,19) to FFT(57344,18) Reduced from FFT(57344,18) to FFT(57344,17) Reduced from FFT(57344,17) to FFT(57344,16) 847698 bit request FFT size=(57344,16) Calling Brillhart-Lehmer-Selfridge with factored part 33.16% 10^127590+10^42297*(9*10^42997-2)/11+1 is PRP! (5836.9091s+0.1726s) [Elapsed time: 1.62 hours] modified 2009-11-24 13:57:51 created 2009-09-01 17:38:02 id 109021