280680 · (21257787 - 1) + 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:280680 · (21257787 - 1) + 1
Verification status (*):Proven
Official Comment (*):[none]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p373 : Morelli, OpenPFGW
Decimal Digits:378638   (log10 is 378637.06336768)
Rank (*):18269 (digit rank is 4)
Entrance Rank (*):2694
Currently on list? (*):no
Submitted:1/10/2014 20:26:38 UTC
Last modified:5/20/2023 20:59:19 UTC
Removed (*):4/28/2015 19:01:21 UTC
Database id:116879
Status Flags:none
Score (*):43.6509 (normalized score 0.2631)

User comments about this prime (disclaimer):

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Serge Batalov writes (11 Sep 2014):  (report abuse)
Use Mersenne#34 (2^1257787-1) as a helper prime for the N-1 proof

With a very low probability, a similar prime (i.e. 2·k·Mp+1) could have been a divisor for the double-Mersenne number 2Mp-1, but this one isn't.

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.
fieldvalue
prime_id116879
person_id9
machineWinXP Dual Core 2.6GHz 64-bit Laptop
whatprime
notesCommand: pfgw64.exe -t -hhelp.txt -q"280680*(2^1257787-1)+1" 2>&1 PFGW Version 3.7.3.64BIT.20130210.Win_Dev [GWNUM 27.8] Primality testing 280680*(2^1257787-1)+1 [N-1, Brillhart-Lehmer-Selfridge] Reading factors from helper file help.txt Running N-1 test using base 17 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 280680*(2^1257787-1)+1 is prime! (11578.6348s+0.0503s) [Elapsed time: 11580 seconds] Helper File: 2^1257787-1
modified2020-07-07 22:30:18
created2014-01-12 05:46:08
id162404

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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