4 · 3416337 - 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:4 · 3416337 - 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):p228 : Jaworski, Srsieve, PRP, OpenPFGW
Decimal Digits:198644   (log10 is 198643.83388621)
Rank (*):34481 (digit rank is 1)
Entrance Rank (*):864
Currently on list? (*):no
Submitted:12/14/2008 15:56:24 UTC
Last modified:3/11/2023 15:54:10 UTC
Removed (*):4/12/2011 17:21:52 UTC
Database id:85940
Status Flags:none
Score (*):41.6674 (normalized score 0.0368)

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_id85940
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 4 3 416337 -1 2>&1 [Elapsed time: 9.435 seconds]
modified2020-07-07 22:30:39
created2008-12-14 16:05:01
id101348

fieldvalue
prime_id85940
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/pfgw -tp -q"4*3^416337-1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 4*3^416337-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 7, base 2+sqrt(7) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(98304,20) to FFT(98304,19) Reduced from FFT(98304,19) to FFT(98304,18) Reduced from FFT(98304,18) to FFT(98304,17) Reduced from FFT(98304,17) to FFT(98304,16) 1319778 bit request FFT size=(98304,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 4*3^416337-1 is prime! (-1951.1857s+0.0500s) [Elapsed time: 10.83 hours]
modified2020-07-07 22:30:39
created2008-12-14 16:08:02
id101349

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