1723856909355 · 2666666 - 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:1723856909355 · 2666666 - 1
Verification status (*):Proven
Official Comment (*):Arithmetic progression (1,d=12521740750545*2^666666) [p199]
Proof-code(s): (*):L934 : Desmond, TwinGen, PrimeGrid, LLR
Decimal Digits:200699   (log10 is 200698.69959054)
Rank (*):34003 (digit rank is 167)
Entrance Rank (*):2676
Currently on list? (*):no
Submitted:9/13/2010 13:25:16 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:94879
Status Flags:none
Score (*):41.699 (normalized score 0.038)

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 17
Subcategory: "Arithmetic progression (1,d=*)"
(archival tag id 213160, tag last modified 2023-03-11 15:53:59)

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_id94879
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 1723856909355 2 666666 -1 2>&1 [Elapsed time: 9.651 seconds]
modified2020-07-07 22:30:33
created2010-09-13 13:35:11
id119139

fieldvalue
prime_id94879
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/llr.pl 1723856909355*2^666666-1 2>&1 Starting Lucas Lehmer Riesel prime test of 1723856909355*2^666666-1 Using Zero Padded IBDWT : Mersenne fftlen = 32768, Used fftlen = 65536 V1 = 9 ; Computing U0... V1 = 9 ; Computing U0...done. Starting Lucas-Lehmer loop... 1723856909355*2^666666-1 is prime! Time : 1334.631 sec. [Elapsed time: 22.25 minutes]
modified2020-07-07 22:30:33
created2010-09-13 13:59:42
id119153

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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