45570624131072 + 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:45570624131072 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L4295 : Splain, GFNSvCUDA, GeneFer, AthGFNSieve, PrimeGrid, LLR
Decimal Digits:1003840   (log10 is 1003839.1570997)
Rank (*):2124 (digit rank is 1)
Entrance Rank (*):231
Currently on list? (*):short
Submitted:3/19/2017 01:34:30 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:123169
Status Flags:none
Score (*):46.6447 (normalized score 6.2717)

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 752
Subcategory: "Generalized Fermat"
(archival tag id 218667, tag last modified 2023-09-24 13:37:27)

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.

PrimeGrid writes (19 Mar 2017):  (report abuse)
For more details, please see the Official Announcement.

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.
machineUsing: Xeon 4c+4c 3.5GHz
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"45570624^131072+1" 2>&1 PFGW Version [GWNUM 27.11] Primality testing 45570624^131072+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Calling Brillhart-Lehmer-Selfridge with factored part 56.59% 45570624^131072+1 is prime! (22248.8015s+0.0249s) [Elapsed time: 6.18 hours]
modified2020-07-07 22:30:16
created2017-03-19 01:41:01

Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.