4283 · 2361409 + 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:4283 · 2361409 + 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):L635 : Vogel, Srsieve, PrimeGrid, LLR
Decimal Digits:108799   (log10 is 108798.581451)
Rank (*):42041 (digit rank is 2)
Entrance Rank (*):4859
Currently on list? (*):no
Submitted:2/8/2009 17:36:23 CDT
Last modified:2/8/2009 19:21:05 CDT
Removed (*):2/21/2009 10:26:37 CDT
Database id:86589
Status Flags:none
Score (*):39.814 (normalized score 0.0096)

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_id86589
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/pfgw -t -q"4283*2^361409+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 4283*2^361409+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(49152,20) to FFT(49152,19) Reduced from FFT(49152,19) to FFT(49152,18) Reduced from FFT(49152,18) to FFT(49152,17) Reduced from FFT(49152,17) to FFT(49152,16) 722852 bit request FFT size=(49152,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 4283*2^361409+1 is prime! (5010.4360s+0.0007s) [Elapsed time: 83.50 minutes]
modified2020-07-07 17:30:38
created2009-02-08 17:38:03
id102595

fieldvalue
prime_id86589
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 4283 2 361409 1 2>&1 [Elapsed time: 13.285 seconds]
modified2020-07-07 17:30:38
created2009-02-08 17:48:02
id102596

Query times: 0.0005 seconds to select prime, 0.0006 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.