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: Phi(3, - 232257316384) Verification status (*): Proven Official Comment: Generalized unique Proof-code(s): (*): p72 : Caldwell, ForEis, PhiSieve, PIES, OpenPFGW Decimal Digits: 208601   (log10 is 208600.08441584) Rank (*): 12145 (digit rank is 1) Entrance Rank (*): 468 Currently on list? (*): short Submitted: 1/17/2008 15:10:06 CDT Last modified: 1/17/2008 18:59:37 CDT Database id: 83711 Status Flags: none Score (*): 41.8178 (normalized score 0.3576)

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 Unique (archivable *)

Prime on list: yes, rank 3
Subcategory: "Generalized Unique"
(archival tag id 209003, tag last modified 2009-05-09 11:50:04)

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 83711 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/pfgw -o -f1{98304} -q"Phi(3,-2322573^16384)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Factoring numbers to 1% of normal. Using modular factorization: {98304} trial factoring to 14024224057 Phi(3,-2322573^16384) has no small factor. [Elapsed time: 18.598 seconds] modified 2011-12-27 16:48:48 created 2008-01-17 15:22:11 id 96552

field value prime_id 83711 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/pfgw -t -q"Phi(3,-2322573^16384)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing Phi(3,-2322573^16384) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 13 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(98304,20) to FFT(98304,19) Reduced from FFT(98304,19) to FFT(98304,18) Reduced from FFT(98304,18) to FFT(98304,17) Reduced from FFT(98304,17) to FFT(98304,16) 1385918 bit request FFT size=(98304,16) Calling Brillhart-Lehmer-Selfridge with factored part 38.07% Phi(3,-2322573^16384) is prime! (11423.9279s+0.8275s) [Elapsed time: 3.17 hours] modified 2008-01-20 07:55:05 created 2008-01-17 15:49:12 id 96556