2 · 467126775 + 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:2 · 467126775 + 1
Verification status (*):Proven
Official Comment (*):Divides Phi(467^126775,2)
Unofficial Comments:This prime has 2 user comments below.
Proof-code(s): (*):g425 : Broadhurst, Keller, Buechel, PRP, OpenPFGW, Proth.exe
Decimal Digits:338403   (log10 is 338402.94856376)
Rank (*):17009 (digit rank is 1)
Entrance Rank (*):342
Currently on list? (*):no
Submitted:1/29/2011 06:41:02 CDT
Last modified:1/29/2011 07:50:22 CDT
Database id:97818
Status Flags:none
Score (*):43.3056 (normalized score 0.26)

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: no, rank 28
Subcategory: "Divides Phi"
(archival tag id 213114, 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)
On 7 December 2006, George Woltman's PRP programme, run by Ingo Buechel and Wilfrid Keller, detected that p=2*467^126775+1 is a probable prime and wrote this finding to a file. However, that file was not inspected by human eye until 28 January 2011. After Wilfrid communicated this to David Broadhurst, it took less than 50 minutes for OpenPFGW to prove that p is prime and less than 18 hours for Yves Gallot's Proth.exe to record that the order of 2 modulo p is the prime power 467^126775, thus allowing p to assume second place in the table of prime divisors of Phi(q^m,2). It might have been in first place for more than 4 years, had the PRP message been read earlier.

David Broadhurst writes (11 Sep 2014):  (report abuse)
Wilfrid Keller has determined that 2*467^n+1 is composite for every positive integer n < 126775.

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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 2 467 126775 1 2>&1 [Elapsed time: 9.162 seconds]
modified2020-07-07 17:30:32
created2011-01-29 06:48:01

machineRedHat Virtual STEM Server
notesCommand: /home/caldwell/client/pfgw -t -q"2*467^126775+1" 2>&1 PFGW Version [GWNUM 25.14] Primality testing 2*467^126775+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 2*467^126775+1 is prime! (1998.5681s+0.0471s) [Elapsed time: 33.30 minutes]
modified2020-07-07 17:30:32
created2011-01-29 06:50:58

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