"((sqrtnint(10⁹⁹⁹⁹⁹⁹, 2048) + 2) + 7748134)²⁰⁴⁸ + 1"

This prime's information:

Description: (from blob table id=449)

190880568043619196745858710869199340262739739165297541288860261919231300520637026081673196260251764084730572923821680257242954091061185112017397561405538291724020883036948742802421424996617325672792384599992465072078363947893924389415971637971808774155203727981089411000649170854300413901434140444900342387223814335592581094310231761182487216832411502606252990491877497417433401295278390481355152602752881480793450415494981527508763542994910431110043260406153080710064791100275825918007972^2048 + 1

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.

Generalized Fermat (archivable *)

Prime on list: no, rank 1488
Subcategory: "Generalized Fermat"
(archival tag id 239062, tag last modified 2025-03-12 10:37:10)

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Jeppe Stig Nielsen writes (26 Feb 2025):  (report abuse)

See description (from blob table) above for a "normal" but lengthy representation as b^2048 + 1. This prime was found, by Gahan, by only considering candidates b^2048 + 1 where b is trivial to a factor (and large enough to give a megaprime). b on FactorDB. To prove this prime, you must first prove that the 484-digit number: 1406387728357690583432986876817654506666026194079879323397927130936542546054028956423869000768115912327448151570994667540324143784895708290482136994234905335268787267078399861501439870594864030479446410362150136100309185905911440787303436665378332307883673690585964243616819212919604593892267693590671822133328035834432974966183075662244608299434230516388059521469139558349543200136146816195773426974985127765122236417251050127529129284392667701438531581784747581194665579413190194203 is prime (can be done with PARI/GP functions isprime or primecert).Then you must make a PFGW helper file containing this 484-digit prime.

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.