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: 1061839 · 2456790-1769267 · 2340000-1 Verification status (*): Proven Official Comment: Arithmetic progression (3,d=1061839*2^456789-1769267*2^340000) Unofficial Comments: This prime has 1 user comment below. Proof-code(s): (*): p97 : Andersen, OpenPFGW Decimal Digits: 137514   (log10 is 137513.51777802) Rank (*): 6388 (digit rank is 7) Entrance Rank (*): 1256 Currently on list? (*): short Submitted: 8/27/2007 10:57:42 CDT Last modified: 8/27/2007 13:42:31 CDT Database id: 82059 Status Flags: none Score (*): 40.5354 (normalized score 0.8413)

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: yes, rank 1, weight 47.4223774784538
Subcategory: "Arithmetic progression (3,d=*)"
(archival tag id 187437, tag last modified 2009-02-12 20:20:07)

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.

Jens Kruse Andersen writes (27 Aug 2007): 

Jens Kruse Andersen found with OpenPFGW that 2 earlier known primes, 1769267*2^340000-1 by Jiong Sun and 1061839*2^456789-1 by Daniel Heuer (both using NewPGen and LLR), are the start of 3 primes in arithmetic progression.

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 82059 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/pfgw -o -f -q"1061839*2^456790-1769267*2^340000-1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 47894502 1061839*2^456790-1769267*2^340000-1 has no small factor. [Elapsed time: 498.625 seconds] modified 2007-09-12 06:50:18 created 2007-08-27 11:22:01 id 93238

field value prime_id 82059 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/pfgw -tp -q"1061839*2^456790-1769267*2^340000-1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 1061839*2^456790-1769267*2^340000-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 3, base 1+sqrt(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) Reduced from FFT(57344,17) to FFT(57344,16) 913638 bit request FFT size=(57344,16) Calling Brillhart-Lehmer-Selfridge with factored part 74.43% 1061839*2^456790-1769267*2^340000-1 is prime! (-847.7946s+0.0000s) [Elapsed time: 2.32444444444444 hours] modified 2007-09-12 06:50:18 created 2007-08-27 11:23:02 id 93239