40078 · 5245766 + 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:40078 · 5245766 + 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):p215 : Lody, Srsieve, SierpinskiRiesel, PRP, OpenPFGW
Decimal Digits:171788   (log10 is 171787.66499169)
Rank (*):32609 (digit rank is 1)
Entrance Rank (*):658
Currently on list? (*):no
Submitted:2/16/2007 02:34:40 CDT
Last modified:2/16/2007 03:51:41 CDT
Removed (*):11/9/2010 12:12:52 CDT
Database id:79408
Status Flags:none
Score (*):41.2204 (normalized score 0.0426)

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_id79408
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 40078 5 245766 1 2>&1 [Elapsed time: 8.717 seconds]
modified2020-07-07 17:30:41
created2007-02-16 02:52:01
id87918

fieldvalue
prime_id79408
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"40078*5^245766+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 40078*5^245766+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(65536,20) to FFT(65536,19) Reduced from FFT(65536,19) to FFT(65536,18) 1141342 bit request FFT size=(65536,18) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 40078*5^245766+1 is prime! (-827.2673s+0.0400s) [Elapsed time: 3520 seconds]
modified2020-07-07 17:30:41
created2007-02-16 02:53:01
id87919

Query times: 0.0005 seconds to select prime, 0.0011 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.