396431486955 · 21000000 - 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:396431486955 · 21000000 - 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):L2832 : Schmidt2, NewPGen, TPS, LLR
Decimal Digits:301042   (log10 is 301041.59383212)
Rank (*):22430 (digit rank is 32)
Entrance Rank (*):1824
Currently on list? (*):no
Submitted:8/12/2012 08:51:19 UTC
Last modified:3/11/2023 15:54:10 UTC
Removed (*):8/19/2013 08:40:33 UTC
Database id:108763
Status Flags:none
Score (*):42.946 (normalized score 0.1324)

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_id108763
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 396431486955 2 1000000 -1 2>&1 [Elapsed time: 9.603 seconds]
modified2020-07-07 22:30:24
created2012-08-12 08:52:02
id147109

fieldvalue
prime_id108763
person_id9
machineRedHat Virtual STEM Server
whatprime
notesCommand: /home/caldwell/client/llr.pl 396431486955*2^1000000-1 2>&1 Starting Lucas Lehmer Riesel prime test of 396431486955*2^1000000-1 Using Zero Padded IBDWT : Mersenne fftlen = 57344, Used fftlen = 114688 V1 = 15 ; Computing U0... V1 = 15 ; Computing U0...done.Starting Lucas-Lehmer loop... 396431486955*2^1000000-1 is prime! Time : 2399.667 sec. [Elapsed time: 40.00 minutes]
modified2020-07-07 22:30:24
created2012-08-12 08:52:35
id147110

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