262 · 17186768 + 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:262 · 17186768 + 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):p231 : Petat, Srsieve, CRUS, PRP, OpenPFGW
Decimal Digits:229811   (log10 is 229810.90244927)
Rank (*):23469 (digit rank is 1)
Entrance Rank (*):424
Currently on list? (*):no
Submitted:6/30/2008 07:38:09 CDT
Last modified:6/30/2008 11:20:18 CDT
Removed (*):5/5/2012 21:25:27 CDT
Database id:85256
Status Flags:none
Score (*):42.1157 (normalized score 0.0961)

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 262 17 186768 1 2>&1 [Elapsed time: 9.103 seconds]
modified2020-07-07 17:30:39
created2008-06-30 07:52:01

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -t -q"262*17^186768+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 262*17^186768+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 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) 1526840 bit request FFT size=(98304,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 262*17^186768+1 is prime! (-1066.4819s+0.0600s) [Elapsed time: 3.45 hours]
modified2020-07-07 17:30:39
created2008-06-30 07:53:01

Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.