3727 · 2450134 + 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:3727 · 2450134 + 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):L828 : Iwata, Srsieve, PrimeGrid, LLR
Decimal Digits:135508   (log10 is 135507.4074276)
Rank (*):43541 (digit rank is 1)
Entrance Rank (*):3494
Currently on list? (*):no
Submitted:5/4/2009 02:07:31 UTC
Last modified:3/11/2023 15:54:10 UTC
Removed (*):9/5/2009 11:53:05 UTC
Database id:88036
Status Flags:none
Score (*):40.4901 (normalized score 0.0116)

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/pfgw -t -q"3727*2^450134+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 3727*2^450134+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(57344,20) to FFT(57344,19) Reduced from FFT(57344,19) to FFT(57344,18) Reduced from FFT(57344,18) to FFT(57344,17) Reduced from FFT(57344,17) to FFT(57344,16) 900300 bit request FFT size=(57344,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 3727*2^450134+1 is prime! (2064.6504s+0.0007s) [Elapsed time: 34.40 minutes]
modified2020-07-07 22:30:38
created2009-05-04 02:08:02

machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 3727 2 450134 1 2>&1 [Elapsed time: 10.048 seconds]
modified2020-07-07 22:30:38
created2009-05-04 02:18:12

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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