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4393 · 21075732 + 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:4393 · 21075732 + 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):L1675 : Schwieger, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:323832   (log10 is 323831.24205681)
Rank (*):14560 (digit rank is 1)
Entrance Rank (*):2585
Currently on list? (*):no
Submitted:4/18/2013 05:42:00 CDT
Last modified:4/18/2013 07:50:31 CDT
Removed (*):12/21/2013 08:50:03 CDT
Database id:113913
Status Flags:none
Score (*):43.1703 (normalized score 0.3611)

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_id113913
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 4393 2 1075732 1 2>&1
[Elapsed time: 10.077 seconds]
modified2013-06-04 07:30:40
created2013-04-18 05:48:02
id158183

fieldvalue
prime_id113913
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"4393*2^1075732+1" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing 4393*2^1075732+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
4393*2^1075732+1 is prime! (2957.5261s+0.0009s)
[Elapsed time: 49.28 minutes]
modified2013-06-04 07:30:40
created2013-04-18 06:46:27
id158186

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.