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: 70583946587 · 2371# + 1 Verification status (*): Proven Official Comment: Arithmetic progression (8,d=59420272*2371#) Proof-code(s): (*): p308 : DavisK, Underwood, NewPGen, PrimeForm_egroup, OpenPFGW Decimal Digits: 1014   (log10 is 1013.5988886315) Rank (*): 105682 (digit rank is 1836) Entrance Rank (*): 100270 Currently on list? (*): no Submitted: 7/3/2012 08:09:11 CDT Last modified: 7/3/2012 09:08:33 CDT Database id: 108130 Status Flags: none Score (*): 25.3142 (normalized score 0)

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.

Arithmetic Progressions of Primes (archivable class *)

Prime on list: no, rank 311, weight 47.9054421467763
Subcategory: "Arithmetic progression (8,d=*)"
(archival tag id 214415, tag last modified 2013-04-14 01:50:41)

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 108130 person_id 9 machine RedHat Virtual STEM Server what prime notes Command: /home/caldwell/client/pfgw -t -q"70583946587*2371#+1" 2>&1 PFGW Version 3.3.4.20100405.x86_Stable [GWNUM 25.14] Primality testing 70583946587*2371#+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Calling Brillhart-Lehmer-Selfridge with factored part 33.56% 70583946587*2371#+1 is prime! (0.3247s+0.0005s) [Elapsed time: 0.00 seconds] modified 2012-07-16 11:32:58 created 2012-07-03 08:22:30 id 145834

field value prime_id 108130 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/TrialDiv/TrialDiv -q 70583946587 2371 # 1 2>&1 [Elapsed time: 143.359 seconds] modified 2012-07-16 11:32:58 created 2012-07-03 09:06:10 id 145861