31 · 21755317 - 1
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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:31 · 21755317 - 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):L330 : Tjung, Srsieve, Rieselprime, LLR
Decimal Digits:528405   (log10 is 528404.56026061)
Rank (*):1850 (digit rank is 1)
Entrance Rank (*):101
Currently on list? (*):yes
Submitted:1/28/2011 12:04:36 CDT
Last modified:1/28/2011 14:20:24 CDT
Database id:97805
Status Flags:none
Score (*):44.6748 (normalized score 2.2448)

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 31 2 1755317 -1 2>&1
[Elapsed time: 10.538 seconds]
modified2011-12-27 16:48:35
created2011-01-28 12:05:01

machineDitto P4 P4
notesCommand: /home/ditto/client/llr.pl 31*2^1755317-1 2>&1
Starting Lucas Lehmer Riesel prime test of 31*2^1755317-1
Using Irrational Base DWT : Mersenne fftlen = 98304, Used fftlen = 114688
V1 = 4 ; Computing U0...
V1 = 4 ; Computing U0...done.
Starting Lucas-Lehmer loop...

31*2^1755317-1 is prime! Time : 6728.830 sec.
[Elapsed time: 1.87 hours]
modified2011-03-25 10:27:31
created2011-01-28 12:08:01

Query times: 0.0005 seconds to select prime, 0.0006 seconds to seek comments.