5166409399321812845 · 10237724 - 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.

This prime's information:

Description:5166409399321812845 · 10237724 - 1
Verification status (*):Proven
Official Comment (*):[none]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p313 : Broadhurst, Srsieve, OpenPFGW
Decimal Digits:237743   (log10 is 237742.71318882)
Rank (*):27600 (digit rank is 1)
Entrance Rank (*):2200
Currently on list? (*):no
Submitted:9/20/2011 17:58:14 UTC
Last modified:3/11/2023 15:54:10 UTC
Removed (*):6/8/2012 01:56:18 UTC
Database id:102111
Status Flags:none
Score (*):42.2201 (normalized score 0.0616)

User comments about this prime (disclaimer):

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David Broadhurst writes (11 Sep 2014):  (report abuse)
5166409399321812845*10^n-1 is prime for 68 values of n < 238000, namely for n = 5, 7, 16, 31, 40, 43, 59, 60, 64, 77, 78, 102, 124, 128, 157, 159, 199, 228, 246, 280, 282, 290, 295, 356, 361, 391, 454, 470, 557, 1024, 1137, 1686, 1733, 1815, 2222, 2357, 2364, 2562, 4495, 4499, 5501, 6316, 7636, 7830, 8455, 15211, 15470, 16127, 16392, 17234, 17306, 20574, 23241, 25532, 27179, 27385, 35469, 43287, 57985, 58507, 74218, 91840, 92176, 93705, 146803, 149340, 200233, 237724

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_id102111
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/pfgw -o -f -q"5166409399321812845*10^237724-1" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] 5166409399321812845*10^237724-1 1/1 mro=0 trial factoring to 85829828 5166409399321812845*10^237724-1 has no small factor. [Elapsed time: 1585.033 seconds]
modified2020-07-07 22:30:30
created2011-09-20 18:05:02
id133788

fieldvalue
prime_id102111
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -tp -q"5166409399321812845*10^237724-1" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 5166409399321812845*10^237724-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 3, base 1+sqrt(3) Calling Brillhart-Lehmer-Selfridge with factored part 69.89% 5166409399321812845*10^237724-1 is prime! (29115.5492s+0.0227s) [Elapsed time: 8.09 hours]
modified2020-07-07 22:30:30
created2011-09-20 18:23:01
id133789

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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