145310262144 + 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:145310262144 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p314 : Hubbard, GenefX64, AthGFNSieve, PrimeGrid, OpenPFGW
Decimal Digits:1353265   (log10 is 1353264.79227886)
Rank (*):221 (digit rank is 1)
Entrance Rank (*):23
Currently on list? (*):short
Submitted:2/9/2011 23:47:24 CDT
Last modified:3/30/2011 22:03:53 CDT
Database id:98160
Status Flags:none
Score (*):47.561 (normalized score 27.9575)

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 56
Subcategory: "Generalized Fermat"
(archival tag id 213124, tag last modified 2020-09-26 16:50:19)

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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.
fieldvalue
prime_id98160
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 1 145310 262144 1 2>&1 [Elapsed time: 8.635 seconds]
modified2020-07-07 17:30:32
created2011-02-09 23:48:01
id125680

fieldvalue
prime_id98160
person_id9
machineXeon 4c+4c 3.5GHz
whatprime
notesCommand: ./pfgw64 -t -q"145310^262144+1" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 145310^262144+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 60.46% 145310^262144+1 is prime! (46438.4777s+0.0465s) [Elapsed time: 12.90 hours]
modified2020-07-07 17:30:17
created2014-08-20 21:18:27
id163950

Query times: 0.0005 seconds to select prime, 0.0009 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.