45870258861 · 2333333 - 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:45870258861 · 2333333 - 1
Verification status (*):Proven
Official Comment (*):Arithmetic progression (3,d=2052418275*2^333336)
Proof-code(s): (*):L1213 : Wolter, NewPGen, PrimeGrid, TPS, LLR
Decimal Digits:100354   (log10 is 100353.89307585)
Rank (*):43510 (digit rank is 3)
Entrance Rank (*):11276
Currently on list? (*):no
Submitted:1/31/2010 10:09:15 CDT
Last modified:1/31/2010 10:50:30 CDT
Database id:91597
Status Flags:none
Score (*):39.5651 (normalized score 0.0077)

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.
Arithmetic Progressions of Primes (archivable class *)
Prime on list: no, rank 30, weight 46.29462160393
Subcategory: "Arithmetic progression (3,d=*)"
(archival tag id 210599, tag last modified 2020-04-18 01:50:22)

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_id91597
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 45870258861 2 333333 -1 2>&1 [Elapsed time: 9.478 seconds]
modified2020-07-07 17:30:36
created2010-01-31 10:18:11
id112566

fieldvalue
prime_id91597
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/llr.pl 45870258861*2^333333-1 2>&1 Starting Lucas Lehmer Riesel prime test of 45870258861*2^333333-1 Using Zero Padded IBDWT : Mersenne fftlen = 16384, Used fftlen = 32768 V1 = 9 ; Computing U0... V1 = 9 ; Computing U0...done. Starting Lucas-Lehmer loop... 45870258861*2^333333-1 is prime! Time : 301.474 sec. [Elapsed time: 5.02 minutes]
modified2020-07-07 17:30:36
created2010-01-31 10:43:03
id112574

Query times: 0.0005 seconds to select prime, 0.001 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.