27 · 1053224 + 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:27 · 1053224 + 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):p67 : Benson, NewPGen, OpenPFGW
Decimal Digits:53226   (log10 is 53225.431363764)
Rank (*):60022 (digit rank is 1)
Entrance Rank (*):3428
Currently on list? (*):no
Submitted:6/13/2004 21:46:40 UTC
Last modified:3/11/2023 15:54:10 UTC
Removed (*):12/13/2004 16:12:04 UTC
Database id:70700
Status Flags:none
Score (*):37.6099 (normalized score 0.0006)

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.
machineLinux P4 2.8GHz
notesCommand: /home/caldwell/client/pfgw -f -t -q"27*10^53224+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 27*10^53224+1 [N-1, Brillhart-Lehmer-Selfridge] trial factoring to 17363072 Running N-1 test using base 11 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(24576,20) to FFT(24576,19) Reduced from FFT(24576,19) to FFT(24576,18) Reduced from FFT(24576,18) to FFT(24576,17) Reduced from FFT(24576,17) to FFT(24576,16) 353632 bit request FFT size=(24576,16) Calling Brillhart-Lehmer-Selfridge with factored part 69.89% 27*10^53224+1 is prime! (921.0303s+0.0045s)
modified2020-07-07 22:30:45
created2004-06-13 21:53:01

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