2 · 3529680 + 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:2 · 3529680 + 1
Verification status (*):Proven
Official Comment (*):[none]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p199 : Broadhurst, NewPGen, OpenPFGW
Decimal Digits:252722   (log10 is 252721.88722991)
Rank (*):19612 (digit rank is 1)
Entrance Rank (*):491
Currently on list? (*):no
Submitted:8/31/2009 07:38:03 CDT
Last modified:8/31/2009 16:50:22 CDT
Removed (*):8/27/2012 08:19:48 CDT
Database id:89804
Status Flags:none
Score (*):42.408 (normalized score 0.1668)

User comments about this prime (disclaimer):

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David Broadhurst writes (11 Sep 2014):  (report abuse)
See the OEIS sequence A003306 for the distribution of primes of this form.

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_id89804
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 2 3 529680 1 2>&1 [Elapsed time: 9.508 seconds]
modified2020-07-07 17:30:37
created2009-08-31 07:48:02
id108978

fieldvalue
prime_id89804
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"2*3^529680+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 2*3^529680+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(114688,20) to FFT(114688,19) Reduced from FFT(114688,19) to FFT(114688,18) Reduced from FFT(114688,18) to FFT(114688,17) Reduced from FFT(114688,17) to FFT(114688,16) 1679056 bit request FFT size=(114688,16) Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(114688,20) to FFT(114688,19) Reduced from FFT(114688,19) to FFT(114688,18) Reduced from FFT(114688,18) to FFT(114688,17) Reduced from FFT(114688,17) to FFT(114688,16) 1679056 bit request FFT size=(114688,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 2*3^529680+1 is prime! (-1327.6111s+0.1000s) [Elapsed time: 8.47 hours]
modified2020-07-07 17:30:37
created2009-08-31 07:53:01
id108979

Query times: 0.0005 seconds to select prime, 0.0007 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.