2 · 191232149 + 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.

Description:2 · 191232149 + 1
Verification status (*):Proven
Official Comment (*):Divides Phi(191^232149,2)
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):g424 : Broadhurst, NewPGen, OpenPFGW, Proth.exe
Decimal Digits:529540   (log10 is 529539.91620319)
Rank (*):3189 (digit rank is 1)
Entrance Rank (*):156
Currently on list? (*):short
Submitted:10/30/2011 09:05:22 CDT
Last modified:10/30/2011 11:20:50 CDT
Database id:102612
Status Flags:none
Score (*):44.6814 (normalized score 1.3419)

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.
Divides Phi (archivable *)
Prime on list: yes, rank 18
Subcategory: "Divides Phi"
(archival tag id 213576, tag last modified 2020-05-22 18:20:06)

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.

David Broadhurst writes (11 Sep 2014):  (report abuse)
Found by OpenPFGW. Proth.exe was used to determine the order of 2 modulo this prime.

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.
machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -t -q"2*191^232149+1" 2>&1 PFGW Version [GWNUM 26.5] Primality testing 2*191^232149+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 2*191^232149+1 is prime! (7879.2345s+0.0403s) [Elapsed time: 2.19 hours]
modified2020-07-07 17:30:30
created2011-10-30 09:08:01

machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 2 191 232149 1 2>&1 [Elapsed time: 9.336 seconds]
modified2020-07-07 17:30:30
created2011-10-30 09:18:02

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