345 · 22313720 - 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:345 · 22313720 - 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):L2017 : Hubbard, PSieve, Srsieve, NPLB, LLR
Decimal Digits:696502   (log10 is 696501.65938676)
Rank (*):3412 (digit rank is 1)
Entrance Rank (*):756
Currently on list? (*):yes
Submitted:10/30/2017 22:35:53 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:123975
Status Flags:none
Score (*):45.5229 (normalized score 2.0892)

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.
machineUsing: Xeon 4c+4c 3.5GHz
notesCommand: /home/caldwell/client/llr.pl 345*2^2313720-1 2>&1 Starting Lucas Lehmer Riesel prime test of 345*2^2313720-1 Using AVX FFT length 144K, Pass1=768, Pass2=192 V1 = 5 ; Computing U0... V1 = 5 ; Computing U0...done.Starting Lucas-Lehmer loop... 345*2^2313720-1 is prime! (696502 decimal digits) Time : 1658.430 sec. [Elapsed time: 27.63 minutes]
modified2020-07-07 22:30:15
created2017-10-30 22:41:02

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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