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: 89 · 2472099+1 Verification status (*): Proven Official Comment: Divides Fermat F(472097) Proof-code(s): (*): p114 : Samidoost, FermFact, PRP, OpenPFGW Decimal Digits: 142118   (log10 is 142117.909312977) Rank (*): 4839 (digit rank is 1) Entrance Rank (*): 223 Currently on list? (*): short Submitted: 10/5/2004 09:59:53 CDT Last modified: 10/5/2004 09:59:53 CDT Database id: 71858 Status Flags: none Score (*): 40.6368 (normalized score 1.0208)

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.

Prime Fermat Divisors (archivable *)

Prime on list: yes, rank 11, weight 45.1254502514641
Subcategory: "Divides Fermat"
(archival tag id 187421, tag last modified 2009-04-01 19:50:37)

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 71858 person_id 9 machine Linux P4 2.8GHz what prime notes Command: /home/caldwell/client/pfgw -f -t -q"89*2^472099+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 89*2^472099+1 [N-1, Brillhart-Lehmer-Selfridge] trial factoring to 49606953 Running N-1 test using base 3 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) 944220 bit request FFT size=(57344,17) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 89*2^472099+1 is prime! (1995.9413s+0.0006s) modified 2004-11-20 19:47:49 created 2004-10-05 12:52:23 id 76855