4043 · 2774709 + 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:4043 · 2774709 + 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):L2121 : VanRangelrooij, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:233215   (log10 is 233214.25361459)
Rank (*):21378 (digit rank is 1)
Entrance Rank (*):3207
Currently on list? (*):no
Submitted:2/26/2012 12:06:55 CDT
Last modified:2/26/2012 15:50:37 CDT
Removed (*):5/20/2012 09:03:33 CDT
Database id:105113
Status Flags:none
Score (*):42.1609 (normalized score 0.1302)

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_id105113
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 4043 2 774709 1 2>&1 [Elapsed time: 10.007 seconds]
modified2020-07-07 17:30:28
created2012-02-26 12:19:45
id139808

fieldvalue
prime_id105113
person_id9
machineRedHat Virtual STEM Server
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"4043*2^774709+1" 2>&1 PFGW Version 3.3.4.20100405.x86_Stable [GWNUM 25.14] Primality testing 4043*2^774709+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 4043*2^774709+1 is prime! (815.9579s+0.0013s) [Elapsed time: 13.67 minutes]
modified2020-07-07 17:30:28
created2012-02-26 15:12:16
id139837

Query times: 0.0005 seconds to select prime, 0.0007 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.