689 · 2875428 - 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:689 · 2875428 - 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):L2017 : Hubbard, PSieve, Srsieve, NPLB, LLR
Decimal Digits:263533   (log10 is 263532.92526335)
Rank (*):25201 (digit rank is 1)
Entrance Rank (*):852
Currently on list? (*):no
Submitted:12/31/2010 04:22:39 UTC
Last modified:3/11/2023 15:54:10 UTC
Removed (*):10/22/2012 00:08:48 UTC
Database id:97173
Status Flags:none
Score (*):42.5368 (normalized score 0.0879)

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_id97173
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/llr.pl 689*2^875428-1 2>&1 Starting Lucas Lehmer Riesel prime test of 689*2^875428-1 Using Irrational Base DWT : Mersenne fftlen = 49152, Used fftlen = 57344 V1 = 4 ; Computing U0... V1 = 4 ; Computing U0...done. Starting Lucas-Lehmer loop... 689*2^875428-1 is prime! Time : 1448.722 sec. [Elapsed time: 24.15 minutes]
modified2020-07-07 22:30:32
created2010-12-31 04:23:01
id123736

fieldvalue
prime_id97173
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 689 2 875428 -1 2>&1 [Elapsed time: 10.184 seconds]
modified2020-07-07 22:30:32
created2010-12-31 04:35:01
id123737

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