41 · 21530313 + 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:41 · 21530313 + 1
Verification status (*):Proven
Official Comment (*):[none]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L2131 : Johnson4, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:460672   (log10 is 460671.72853839)
Rank (*):11027 (digit rank is 1)
Entrance Rank (*):184
Currently on list? (*):no
Submitted:7/20/2011 05:24:44 UTC
Last modified:3/11/2023 15:54:10 UTC
Removed (*):12/8/2020 15:07:58 UTC
Database id:100855
Status Flags:none
Score (*):44.2534 (normalized score 0.4897)

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.

PrimeGrid writes (11 Sep 2014):  (report abuse)
41*2^1530313+1 Divides xGF(1530311,7,6)
41*2^1530313+1 Divides xGF(1530310,9,8)

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_id100855
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 41 2 1530313 1 2>&1 [Elapsed time: 10.316 seconds]
modified2020-07-07 22:30:31
created2011-07-20 05:35:21
id131277

fieldvalue
prime_id100855
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"41*2^1530313+1" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 41*2^1530313+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 41*2^1530313+1 is prime! (4776.5825s+0.0013s) [Elapsed time: 79.62 minutes]
modified2020-07-07 22:30:31
created2011-07-20 07:14:06
id131300

Query times: 0.0016 seconds to select prime, 0.0094 seconds to seek comments.
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