2^15317227 + 2^7658614 + 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.

Gaussian Mersenne norm (archivable *)

Prime on list: yes, rank 1
Subcategory: "Gaussian Mersenne norm"
(archival tag id 224076, tag last modified 2023-03-11 15:53:59)

Generalized Unique (archivable *)

Prime on list: yes, rank 4
Subcategory: "Generalized Unique"
(archival tag id 224078, tag last modified 2023-12-14 08:37:23)

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Serge Batalov writes (31 Jul 2020):  (report abuse)

This is also a Generalized Unique number (all Gaussian Mersenne norms are, as well). To recognize the Generalized Unique property, we can write this number as: Phi(4, 27658614 + 1)/2

Serge Batalov writes (31 Jul 2020):  (report abuse)

A note on double-checking: one may want to use a 4-/8-threaded LLR with the following input (this will take care of a much faster FFT modulus): ABC 4^$a+1 15317227

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.