217 · 22264546 + 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:217 · 22264546 + 1
Verification status (*):Proven
Official Comment (*):[none]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L3179 : Hamada, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:681699   (log10 is 681698.60902062)
Rank (*):4074 (digit rank is 1)
Entrance Rank (*):269
Currently on list? (*):yes
Submitted:9/18/2014 16:46:15 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:118515
Status Flags:none
Score (*):45.457 (normalized score 1.6463)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

Masumi Hamada writes (18 Sep 2014):  (report abuse)
Divides GF(2264543,7)!

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_id118515
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"217*2^2264546+1" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 217*2^2264546+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 217*2^2264546+1 is prime! (1918.0718s+0.0009s) [Elapsed time: 31.97 minutes]
modified2020-07-07 22:30:17
created2014-09-18 16:51:00
id164094

Query times: 0.0004 seconds to select prime, 0.0005 seconds to seek comments.
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