165 · 22717378 - 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:165 · 22717378 - 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):L2055 : Soule, PSieve, Srsieve, Rieselprime, LLR
Decimal Digits:818015   (log10 is 818014.50504134)
Rank (*):3411 (digit rank is 1)
Entrance Rank (*):65
Currently on list? (*):short
Submitted:2/28/2012 16:07:28 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:105208
Status Flags:none
Score (*):46.0166 (normalized score 2.8564)

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_id105208
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/llr.pl 165*2^2717378-1 2>&1 Starting Lucas Lehmer Riesel prime test of 165*2^2717378-1 Using Irrational Base DWT : Mersenne fftlen = 163840, Used fftlen = 196608 V1 = 5 ; Computing U0... V1 = 5 ; Computing U0...done. Starting Lucas-Lehmer loop... 165*2^2717378-1 is prime! Time : 16010.112 sec. [Elapsed time: 4.45 hours]
modified2020-07-07 22:30:28
created2012-02-28 16:08:02
id140005

fieldvalue
prime_id105208
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 165 2 2717378 -1 2>&1 [Elapsed time: 10.723 seconds]
modified2020-07-07 22:30:28
created2012-02-28 16:18:02
id140006

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