2 · 659233973 + 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 · 659233973 + 1
Verification status (*):Proven
Official Comment (*):Divides Phi(659^233973,2)
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):g424 : Broadhurst, NewPGen, OpenPFGW, Proth.exe
Decimal Digits:659544   (log10 is 659543.3781388)
Rank (*):2132 (digit rank is 1)
Entrance Rank (*):390
Currently on list? (*):short
Submitted:3/4/2015 05:53:49 CDT
Last modified:3/4/2015 06:50:25 CDT
Database id:119495
Status Flags:TrialDiv
Score (*):45.3555 (normalized score 2.6664)

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 15
Subcategory: "Divides Phi"
(archival tag id 217912, tag last modified 2020-05-22 18:20:06)

User comments about this prime (disclaimer):

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David Broadhurst writes (4 Mar 2015):  (report abuse)
Found by OpenPFGW. The order of 2 modulo this prime was confirmed by Serge Batalov's program sllr64_DivPhi.

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 4c+4c 3.5GHz
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"2*659^233973+1" 2>&1 PFGW Version [GWNUM 27.11] Primality testing 2*659^233973+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 17 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 2*659^233973+1 is prime! (2420.8511s+0.0209s) [Elapsed time: 40.35 minutes]
modified2020-07-07 17:30:17
created2015-03-04 06:01:02

Query times: 0.0006 seconds to select prime, 0.0008 seconds to seek comments.
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