319 · 21740047 - 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:319 · 21740047 - 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):L1819 : Gunn, PSieve, Srsieve, NPLB, LLR
Decimal Digits:523809   (log10 is 523808.8446558)
Rank (*):4901 (digit rank is 1)
Entrance Rank (*):399
Currently on list? (*):yes
Submitted:6/13/2013 21:03:53 CDT
Last modified:6/17/2013 18:25:30 CDT
Database id:114400
Status Flags:none
Score (*):44.648 (normalized score 1.0132)

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.
machineDitto P4 P4
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 319 2 1740047 -1 2>&1 [Elapsed time: 10.699 seconds]
modified2020-07-07 17:30:19
created2013-06-13 21:05:01

machineDitto P4 P4
notesCommand: /home/ditto/client/llr.pl 319*2^1740047-1 2>&1 Starting Lucas Lehmer Riesel prime test of 319*2^1740047-1 Using Irrational Base DWT : Mersenne fftlen = 98304, Used fftlen = 114688 V1 = 4 ; Computing U0... V1 = 4 ; Computing U0...done. Starting Lucas-Lehmer loop... 319*2^1740047-1 is prime! Time : 6035.699 sec. [Elapsed time: 1.68 hours]
modified2020-07-07 17:30:19
created2013-06-13 21:08:02

Query times: -0.9997 seconds to select prime, 0.0004 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.