19540909 · 2690774 + 1
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At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: 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:

field (help)value
Description:19540909 · 2690774 + 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):g393 : Tamai, NewPGen, PRP, Proth.exe
Decimal Digits:207951   (log10 is 207950.985169553)
Rank (*):20941 (digit rank is 1)
Entrance Rank (*):166
Currently on list? (*):no
Submitted:7/6/2005 02:12:34 CDT
Last modified:7/6/2005 02:12:34 CDT
Removed (*):1/25/2012 23:06:53 CDT
Database id:74990
Status Flags:none
Score (*):41.8082 (normalized score 0.1448)

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.
fieldvalue
prime_id74990
person_id9
machineLinux P4 2.8GHz
whatprime
notesCommand: /home/caldwell/client/pfgw -f -t -q"19540909*2^690774+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 19540909*2^690774+1 [N-1, Brillhart-Lehmer-Selfridge]
trial factoring to 74427000
Running N-1 test using base 3
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(98304,20) to FFT(98304,19)
Reduced from FFT(98304,19) to FFT(98304,18)
Reduced from FFT(98304,18) to FFT(98304,17)
Reduced from FFT(98304,17) to FFT(98304,16)
1381606 bit request FFT size=(98304,16)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
19540909*2^690774+1 is prime! (10115.6308s+0.0006s)
modified2005-07-15 09:51:51
created2005-07-06 02:23:00
id80086

Query times: 0.0004 seconds to select prime, 0.0005 seconds to seek comments.