342924651 · 23394939 - 1
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GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits)

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: 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:

field (help)value
Description:342924651 · 23394939 - 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):L4166 : Kwok, PSieve, LLR
Decimal Digits:1021988   (log10 is 1021987.00764819)
Rank (*):350 (digit rank is 1)
Entrance Rank (*):242
Currently on list? (*):short
Submitted:12/21/2017 11:00:38 CDT
Last modified:12/21/2017 13:20:21 CDT
Database id:124074
Status Flags:TrialDiv
Score (*):46.6997 (normalized score 14.9455)

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_id124074
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/client/llr.pl 342924651*2^3394939-1 2>&1
Starting Lucas Lehmer Riesel prime test of 342924651*2^3394939-1
Using zero-padded AVX FFT length 384K, Pass1=384, Pass2=1K
V1 = 3 ; Computing U0...
V1 = 3 ; Computing U0...done.Starting Lucas-Lehmer loop...


342924651*2^3394939-1 is prime! (1021988 decimal digits) Time : 6780.782 sec.
[Elapsed time: 1.88 hours]
modified2018-09-25 13:41:14
created2017-12-21 11:01:01
id169737

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