214519 · 21929114 + 1
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GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits)

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:214519 · 21929114 + 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):g346 : Dausch, ProthSieve, PrimeSierpinski, PRP, Proth.exe
Decimal Digits:580727   (log10 is 580726.510521089)
Rank (*):1861 (digit rank is 1)
Entrance Rank (*):23
Currently on list? (*):yes
Submitted:1/2/2006 14:19:59 CDT
Last modified:1/3/2006 05:06:29 CDT
Database id:76631
Status Flags:none
Score (*):44.9648 (normalized score 2.5256)

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"214519*2^1929114+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 214519*2^1929114+1 [N-1, Brillhart-Lehmer-Selfridge]
trial factoring to 221713948
Running N-1 test using base 3
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(262144,19) to FFT(262144,18)
Reduced from FFT(262144,18) to FFT(262144,17)
Reduced from FFT(262144,17) to FFT(262144,16)
3858272 bit request FFT size=(262144,16)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
214519*2^1929114+1 is prime! (-1939.8530s+0.0000s)
[Elapsed time: 52236 seconds]
modified2006-01-03 11:23:37
created2006-01-02 14:35:53

machineLinux P4 2.8GHz
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 214519 2 1929114 1 2>&1
[Elapsed time: 17.684 seconds]
modified2006-01-02 22:51:02
created2006-01-02 14:22:00

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