35 · 21357881 + 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:35 · 21357881 + 1
Verification status (*):Proven
Official Comment (*):[none]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):g279 : Cooper, NewPGen, PRP, Proth.exe
Decimal Digits:408765   (log10 is 408764.45561025)
Rank (*):12143 (digit rank is 1)
Entrance Rank (*):60
Currently on list? (*):no
Submitted:8/22/2006 02:43:52 UTC
Last modified:3/11/2023 15:54:10 UTC
Removed (*):9/26/2018 20:14:38 UTC
Database id:78358
Status Flags:none
Score (*):43.8861 (normalized score 0.3975)

User comments about this prime (disclaimer):

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Curtis Cooper writes (11 Sep 2014):  (report abuse)
35*2^1357881+1 is a Factor of xGF(1357878,7,5)

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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 35 2 1357881 1 2>&1 [Elapsed time: 10.116 seconds]
modified2020-07-07 22:30:42
created2006-08-22 02:52:02

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -t -q"35*2^1357881+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 35*2^1357881+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(196608,19) to FFT(196608,18) Reduced from FFT(196608,18) to FFT(196608,17) Reduced from FFT(196608,17) to FFT(196608,16) 2715782 bit request FFT size=(196608,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 35*2^1357881+1 is prime! (13384.7096s+0.0013s) [Elapsed time: 13385 seconds]
modified2020-07-07 22:30:42
created2006-08-22 02:53:01

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