825 · 2373331 + 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:825 · 2373331 + 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):L646 : Strang, Srsieve, PrimeGrid, LLR
Decimal Digits:112387   (log10 is 112386.74576518)
Rank (*):45135 (digit rank is 1)
Entrance Rank (*):3949
Currently on list? (*):no
Submitted:11/26/2008 13:52:44 UTC
Last modified:3/11/2023 15:54:10 UTC
Removed (*):3/24/2009 23:05:58 UTC
Database id:85825
Status Flags:none
Score (*):39.914 (normalized score 0.0073)

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"825*2^373331+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 825*2^373331+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 17 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(49152,20) to FFT(49152,19) Reduced from FFT(49152,19) to FFT(49152,18) Reduced from FFT(49152,18) to FFT(49152,17) Reduced from FFT(49152,17) to FFT(49152,16) 746690 bit request FFT size=(49152,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 825*2^373331+1 is prime! (757.2000s+0.0000s) [Elapsed time: 13.18 minutes]
modified2020-07-07 22:30:39
created2008-11-26 13:53:02

machineDitto P4 P4
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 825 2 373331 1 2>&1 [Elapsed time: 9.777 seconds]
modified2020-07-07 22:30:39
created2008-11-26 14:05:01

Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
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