4123 · 2704766 + 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:4123 · 2704766 + 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):L2085 : Dodson1, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:212160   (log10 is 212159.32113746)
Rank (*):28713 (digit rank is 1)
Entrance Rank (*):3091
Currently on list? (*):no
Submitted:9/5/2011 12:34:58 UTC
Last modified:3/11/2023 15:54:10 UTC
Removed (*):2/19/2012 15:00:59 UTC
Database id:101799
Status Flags:none
Score (*):41.8699 (normalized score 0.0524)

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 4123 2 704766 1 2>&1 [Elapsed time: 10.122 seconds]
modified2020-07-07 22:30:31
created2011-09-05 12:35:11

machineRedHat Virtual STEM Server
notesCommand: /home/caldwell/client/pfgw -t -q"4123*2^704766+1" 2>&1 PFGW Version [GWNUM 25.14] Primality testing 4123*2^704766+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 4123*2^704766+1 is prime! (863.4714s+0.0215s) [Elapsed time: 14.38 minutes]
modified2020-07-07 22:30:31
created2011-09-05 12:52:43

Query times: 0.0002 seconds to select prime, 0.0005 seconds to seek comments.
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