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2697 · 2743822 + 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:2697 · 2743822 + 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):L1547 : Shewbridge, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:223917   (log10 is 223916.16431572)
Rank (*):22168 (digit rank is 1)
Entrance Rank (*):3073
Currently on list? (*):no
Submitted:12/10/2011 10:41:14 CDT
Last modified:12/10/2011 11:20:51 CDT
Removed (*):4/12/2012 11:38:05 CDT
Database id:103581
Status Flags:none
Score (*):42.0358 (normalized score 0.1155)

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_id103581
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 2697 2 743822 1 2>&1 [Elapsed time: 10.261 seconds]
modified2020-07-07 17:30:30
created2011-12-10 10:48:02
id136744

fieldvalue
prime_id103581
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"2697*2^743822+1" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 2697*2^743822+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 41 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 2697*2^743822+1 is prime! (1430.2980s+0.0006s) [Elapsed time: 23.83 minutes]
modified2020-07-07 17:30:29
created2011-12-10 10:53:01
id136749

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.