205833 · 22976222 - 411665

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:205833 · 22976222 - 411665
Verification status (*):Proven
Official Comment (*):[none]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L4667 : Morelli, LLR
Decimal Digits:895938   (log10 is 895937.40927005)
Rank (*):3221 (digit rank is 1)
Entrance Rank (*):349
Currently on list? (*):short
Submitted:8/20/2017 10:23:00 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:123859
Status Flags:none
Score (*):46.2958 (normalized score 3.5507)

User comments about this prime (disclaimer):

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Luigi Morelli writes (1 Sep 2017):  (report abuse)
This number can also be written as 411666*(22976221-1)+1. Use Mersenne#36 (22976221-1) as a helper prime for the N-1 proof.

With a very low probability, a similar prime (i.e. of the form 2*k*Mp+1) could be 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.
machineUsing: Xeon (pool) 4c+4c 3.5GHz
notesCommand: /home/caldwell/clientpool/1/pfgw64 -t -hhelper -q"205833*2^2976222-411665" 2>&1 PFGW Version [GWNUM 27.11] Primality testing 205833*2^2976222-411665 [N-1, Brillhart-Lehmer-Selfridge] Reading factors from helper file helper Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 205833*2^2976222-411665 is prime! (35295.7567s+0.0011s) [Elapsed time: 9.80 hours] Helper File: 2^2976221-1
modified2020-07-07 22:30:15
created2017-08-26 17:13:44

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