46821 · 23021380 - 374567

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.

Description:46821 · 23021380 - 374567
Verification status (*):Proven
Official Comment (*):[none]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p363 : Batalov, OpenPFGW
Decimal Digits:909531   (log10 is 909530.67873993)
Rank (*):910 (digit rank is 2)
Entrance Rank (*):85
Currently on list? (*):short
Submitted:9/8/2013 20:04:11 CDT
Last modified:9/15/2013 11:56:04 CDT
Database id:115433
Status Flags:Verify, TrialDiv
Score (*):46.342 (normalized score 8.2999)

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.

Serge Batalov writes (11 Sep 2014):  (report abuse)
Also can be written as 374568*(2^3021377-1)+1
Use Mersenne#37 (2^3021377-1) 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_id115433
person_id9
machineRedHat Virtual STEM Server
whatprime
notesPFGW Version 3.3.4.20100405.x86_Stable [GWNUM 25.14] Primality testing 46821*2^3021380-374567 [N-1, Brillhart-Lehmer-Selfridge] Reading factors from helper file helper: 2^3021377-1 trial factoring to 3567360 Running N-1 test using base 11 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 46821*2^3021380-374567 is prime! (111545.6590s+0.0429s)
modified2020-07-07 17:30:18
created2013-09-08 20:58:07
id160918

Query times: 0.0017 seconds to select prime, 0.0006 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.