215 · 2953677 + 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:215 · 2953677 + 1
Verification status (*):Proven
Official Comment (*):[none]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L669 : Harvey, Srsieve, PrimeGrid, LLR
Decimal Digits:287088   (log10 is 287087.7156133)
Rank (*):17229 (digit rank is 1)
Entrance Rank (*):429
Currently on list? (*):no
Submitted:5/24/2010 18:06:36 CDT
Last modified:5/24/2010 19:50:22 CDT
Removed (*):5/10/2013 12:15:01 CDT
Database id:92839
Status Flags:none
Score (*):42.8 (normalized score 0.2397)

User comments about this prime (disclaimer):

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Steven Harvey writes (11 Sep 2014):  (report abuse)
215*2^953677+1 is a Factor of xGF(953676,5,3)

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_id92839
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/pfgw -t -q"215*2^953677+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 215*2^953677+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(114688,20) to FFT(114688,19) Reduced from FFT(114688,19) to FFT(114688,18) Reduced from FFT(114688,18) to FFT(114688,17) 1907378 bit request FFT size=(114688,17) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 215*2^953677+1 is prime! (4832.5374s+0.0008s) [Elapsed time: 80.55 minutes]
modified2020-07-07 17:30:34
created2010-05-24 18:08:01
id115058

fieldvalue
prime_id92839
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 215 2 953677 1 2>&1 [Elapsed time: 10.047 seconds]
modified2020-07-07 17:30:34
created2010-05-24 18:18:01
id115059

Query times: 0.0005 seconds to select prime, 0.0008 seconds to seek comments.
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