34419644919 · 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.

This prime's information:

Description:34419644919 · 2333333 - 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):L573 : Pierre, NewPGen, PrimeGrid, TPS, LLR
Decimal Digits:100354   (log10 is 100353.76835105)
Rank (*):48987 (digit rank is 232)
Entrance Rank (*):4601
Currently on list? (*):no
Submitted:2/23/2008 14:07:17 UTC
Last modified:3/11/2023 15:54:10 UTC
Removed (*):4/11/2008 17:06:35 UTC
Database id:84181
Status Flags:none
Score (*):39.5651 (normalized score 0.0042)

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/llr.pl 34419644919*2^333333-1 2>&1 Starting Lucas Lehmer Riesel prime test of 34419644919*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 : 301.844 sec. [Elapsed time: 5.02 minutes]
modified2020-07-07 22:30:40
created2008-02-23 14:08:02

machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 34419644919 2 333333 -1 2>&1 [Elapsed time: 9.245 seconds]
modified2020-07-07 22:30:40
created2008-02-23 14:22:01

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