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8063 · 2453497 + 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:8063 · 2453497 + 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):L714 : Sunderland, Srsieve, PrimeGrid, LLR
Decimal Digits:136521   (log10 is 136520.10644029)
Rank (*):37053 (digit rank is 1)
Entrance Rank (*):3388
Currently on list? (*):no
Submitted:5/3/2009 22:22:09 CDT
Last modified:5/3/2009 23:20:21 CDT
Removed (*):9/21/2009 09:28:18 CDT
Database id:88040
Status Flags:none
Score (*):40.513 (normalized score 0.0253)

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_id88040
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 8063 2 453497 1 2>&1
[Elapsed time: 14.223 seconds]
modified2011-12-27 16:48:44
created2009-05-03 22:35:01
id105440

fieldvalue
prime_id88040
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"8063*2^453497+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 8063*2^453497+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(57344,20) to FFT(57344,19)
Reduced from FFT(57344,19) to FFT(57344,18)
Reduced from FFT(57344,18) to FFT(57344,17)
Reduced from FFT(57344,17) to FFT(57344,16)
907028 bit request FFT size=(57344,16)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
8063*2^453497+1 is prime! (1928.4942s+0.0007s)
[Elapsed time: 32.15 minutes]
modified2009-05-25 07:25:56
created2009-05-03 22:23:01
id105439

Query times: 0.0005 seconds to select prime, 0.0009 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.