45 · 22507894 + 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:45 · 22507894 + 1
Verification status (*):Proven
Official Comment (*):[none]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L1349 : Wallace, Srsieve, NewPGen, PrimeGrid, LLR
Decimal Digits:754953   (log10 is 754952.97315824)
Rank (*):3829 (digit rank is 1)
Entrance Rank (*):84
Currently on list? (*):yes
Submitted:4/16/2012 16:29:40 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:106341
Status Flags:none
Score (*):45.7703 (normalized score 2.0899)

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.

Darren Wallace writes (11 Sep 2014):  (report abuse)
45*2^2507894+1 is a Factor of xGF(2507891,5,3)!!!!
45*2^2507894+1 is a Factor of GF(2507890,8)!!!!
45*2^2507894+1 is a Factor of xGF(2507893,9,7)!!!!
45*2^2507894+1 is a Factor of xGF(2507884,11,7)!!!!
45*2^2507894+1 is a Factor of xGF(2507893,11,9)!!!!

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.
machineDitto P4 P4
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 45 2 2507894 1 2>&1 [Elapsed time: 10.621 seconds]
modified2020-07-07 22:30:26
created2012-04-16 16:35:01

machineRedHat Virtual STEM Server
notesCommand: /home/caldwell/client/pfgw -t -q"45*2^2507894+1" 2>&1 PFGW Version [GWNUM 25.14] Primality testing 45*2^2507894+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 45*2^2507894+1 is prime! (8967.7758s+0.0341s) [Elapsed time: 2.49 hours]
modified2020-07-07 22:30:26
created2012-04-16 16:35:16

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