31613415669 · 2333333 - 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.

Description:31613415669 · 2333333 - 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):L493 : Simpson, NewPGen, PrimeGrid, TPS, LLR
Decimal Digits:100354   (log10 is 100353.73141608)
Rank (*):42692 (digit rank is 475)
Entrance Rank (*):4470
Currently on list? (*):no
Submitted:1/31/2008 14:41:28 CDT
Last modified:1/31/2008 15:13:09 CDT
Removed (*):3/11/2008 09:55:17 CDT
Database id:83816
Status Flags:none
Score (*):39.5651 (normalized score 0.0093)

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_id83816
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 31613415669 2 333333 -1 2>&1 [Elapsed time: 9.647 seconds]
modified2020-07-07 17:30:40
created2008-01-31 14:53:17
id96770

fieldvalue
prime_id83816
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/llr.pl 31613415669*2^333333-1 2>&1 Starting Lucas Lehmer Riesel prime test of 31613415669*2^333333-1 Using Zero Padded IBDWT : Mersenne fftlen = 16384, Used fftlen = 32768 V1 = 3 ; Computing U0... V1 = 3 ; Computing U0...done. Starting Lucas-Lehmer loop... *2^333333-1 is prime! Time : 308.137 sec. [Elapsed time: 5.13 minutes]
modified2020-07-07 17:30:40
created2008-01-31 15:08:01
id96771

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.