2 · 47³⁴⁶⁷⁵⁹ + 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: yes, rank 17
Subcategory: "Divides Phi"
(archival tag id 213110, tag last modified 2023-03-11 15:53:59)

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David Broadhurst writes (11 Sep 2014):  (report abuse)

OpenPFGW found that 2*47^n+1 is prime for n=346759 and that the only smaller positive integer yielding a prime is n=175. Proth.exe found that the order of 2, modulo p=2*47^346759+1, is a prime power, namely (p-1)/2. With 579816 decimal digits, p more than doubled the number of digits of the previous record for this form of prime, which was 2*827^98511+1, with 287407 digits. I thank Wilfrid Keller for encouragement, over the last 7 years, to find a large prime of this form.

Verification data:

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