321 · 2730321 + 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:321 · 2730321 + 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):L1273 : Davies, Srsieve, PrimeGrid, LLR
Decimal Digits:219852   (log10 is 219851.03396835)
Rank (*):20048 (digit rank is 1)
Entrance Rank (*):1011
Currently on list? (*):no
Submitted:2/19/2010 05:44:24 CDT
Last modified:2/19/2010 06:50:20 CDT
Removed (*):3/24/2012 08:07:58 CDT
Database id:91910
Status Flags:none
Score (*):41.9794 (normalized score 0.1599)

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/TrialDiv/TrialDiv -q 321 2 730321 1 2>&1
[Elapsed time: 9.618 seconds]
modified2011-12-27 16:48:40
created2010-02-19 05:48:01

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -t -q"321*2^730321+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 321*2^730321+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
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)
1460668 bit request FFT size=(98304,16)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
321*2^730321+1 is prime! (-1187.4373s+0.0000s)
[Elapsed time: 51.98 minutes]
modified2010-03-13 18:56:30
created2010-02-19 05:53:02

Query times: 0.0005 seconds to select prime, 0.0006 seconds to seek comments.