1061839 · 2456790 - 1769267 · 2340000 - 1

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly.  This list is the most important PrimePages database: 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:

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 (*):41647 (digit rank is 7)
Entrance Rank (*):1256
Currently on list? (*):no
Submitted:8/27/2007 15:57:42 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:82059
Status Flags:none
Score (*):40.5354 (normalized score 0.0142)

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 31, weight 47.422376103147
Subcategory: "Arithmetic progression (3,d=*)"
(archival tag id 187437, tag last modified 2023-03-11 16:02:30)

User comments about this prime (disclaimer):

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Jens Kruse Andersen writes (11 Sep 2014):  (report abuse)
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.
machineRedHat P4 P4
notesCommand: /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]
modified2020-07-07 22:30:40
created2007-08-27 16:22:01

machineRedHat P4 P4
notesCommand: /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]
modified2020-07-07 22:30:40
created2007-08-27 16:23:02

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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