40734262144 + 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.

Description:40734262144 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p309 : Yama, GenefX64, AthGFNSieve, PrimeGrid, OpenPFGW
Decimal Digits:1208473   (log10 is 1208472.5832897)
Rank (*):348 (digit rank is 1)
Entrance Rank (*):26
Currently on list? (*):short
Submitted:3/8/2011 17:00:26 CDT
Last modified:3/9/2011 04:20:21 CDT
Database id:99092
Status Flags:none
Score (*):47.2139 (normalized score 15.9501)

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 71
Subcategory: "Generalized Fermat"
(archival tag id 213162, tag last modified 2021-10-09 23:37:19)

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 (11 Sep 2014):  (report abuse)
For more information, 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.
machineDitto P4 P4
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 1 40734 262144 1 2>&1 [Elapsed time: 8.487 seconds]
modified2020-07-07 17:30:32
created2011-03-08 17:05:21

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -t -q"40734^262144+1" 2>&1 PFGW Version [GWNUM 26.5] Primality testing 40734^262144+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Calling Brillhart-Lehmer-Selfridge with factored part 40.42% 40734^262144+1 is prime! (39294.0328s+0.0909s) [Elapsed time: 10.92 hours]
modified2020-07-07 17:30:32
created2011-03-08 17:23:01

Query times: 0.0004 seconds to select prime, 0.0008 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.