(264 - 189) · 10413500 + 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:(264 - 189) · 10413500 + 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):p342 : Trice, OpenPFGW
Decimal Digits:413520   (log10 is 413519.26591972)
Rank (*):13458 (digit rank is 2)
Entrance Rank (*):657
Currently on list? (*):no
Submitted:12/1/2012 05:20:22 UTC
Last modified:3/11/2023 15:54:10 UTC
Removed (*):1/16/2019 13:06:47 UTC
Database id:110196
Status Flags:none
Score (*):43.9217 (normalized score 0.3391)

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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -t -q"(2^64-189)*10^413500+1" 2>&1 PFGW Version [GWNUM 26.5] Primality testing (2^64-189)*10^413500+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 69.89% (2^64-189)*10^413500+1 is prime! (28822.7063s+0.0201s) [Elapsed time: 8.01 hours]
modified2020-07-07 22:30:23
created2012-12-01 05:23:02

machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -o -f -q"(2^64-189)*10^413500+1" 2>&1 PFGW Version [GWNUM 26.5] (2^64-189)*10^413500+1 1/1 mro=0 trial factoring to 154611114 (2^64-189)*10^413500+1 has no small factor. [Elapsed time: 4328.691 seconds]
modified2020-07-07 22:30:23
created2012-12-01 05:35:01

Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.
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