287626 · 5277175 - 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:287626 · 5277175 - 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):p212 : Pinho, Srsieve, SierpinskiRiesel, PRP, OpenPFGW
Decimal Digits:193743   (log10 is 193742.46977998)
Rank (*):30341 (digit rank is 1)
Entrance Rank (*):841
Currently on list? (*):no
Submitted:8/13/2008 01:00:38 CDT
Last modified:8/13/2008 18:30:00 CDT
Removed (*):2/26/2011 13:04:35 CDT
Database id:85415
Status Flags:none
Score (*):41.5905 (normalized score 0.0577)

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_id85415
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 287626 5 277175 -1 2>&1 [Elapsed time: 9.989 seconds]
modified2020-07-07 17:30:39
created2008-08-13 01:05:01
id100297

fieldvalue
prime_id85415
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/pfgw -tp -q"287626*5^277175-1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 287626*5^277175-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 11, base 8+sqrt(11) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(81920,20) to FFT(81920,19) Reduced from FFT(81920,19) to FFT(81920,18) Reduced from FFT(81920,18) to FFT(81920,17) Reduced from FFT(81920,17) to FFT(81920,16) 1287214 bit request FFT size=(81920,16) Running N+1 test using discriminant 11, base 10+sqrt(11) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(81920,20) to FFT(81920,19) Reduced from FFT(81920,19) to FFT(81920,18) Reduced from FFT(81920,18) to FFT(81920,17) Reduced from FFT(81920,17) to FFT(81920,16) 1287214 bit request FFT size=(81920,16) Running N+1 test using discriminant 11, base 11+sqrt(11) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(81920,20) to FFT(81920,19) Reduced from FFT(81920,19) to FFT(81920,18) Reduced from FFT(81920,18) to FFT(81920,17) Reduced from FFT(81920,17) to FFT(81920,16) 1287214 bit request FFT size=(81920,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 287626*5^277175-1 is prime! (-1824.3621s+0.0400s) [Elapsed time: 17.37 hours]
modified2020-07-07 17:30:39
created2008-08-13 01:08:01
id100298

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.