2 · 467¹²⁶⁷⁷⁵ + 1

This prime's information:

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 2023-03-11 15:53:59)

User comments about this prime (disclaimer):

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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.