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: 489 · 2704557 + 1 Verification status (*): Proven Official Comment: Unofficial Comments: This prime has 1 user comment below. Proof-code(s): (*): L689 : Brown1, Srsieve, PrimeGrid, LLR Decimal Digits: 212096   (log10 is 212095.47996389) Rank (*): 21844 (digit rank is 1) Entrance Rank (*): 1019 Currently on list? (*): no Submitted: 1/31/2010 20:14:19 CDT Last modified: 2/7/2010 19:11:32 CDT Removed (*): 2/19/2012 08:50:08 CDT Database id: 91605 Status Flags: none Score (*): 41.8689 (normalized score 0.1246)

User comments about this prime (disclaimer):

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Dr. James Scott Brown writes (11 Sep 2014): 

Divides xGF(704554,10,3)

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.

field value prime_id 91605 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 489 2 704557 1 2>&1 [Elapsed time: 9.737 seconds] modified 2011-12-27 16:48:40 created 2010-01-31 20:18:01 id 112585

field value prime_id 91605 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/pfgw -t -q"489*2^704557+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 489*2^704557+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 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) 1409140 bit request FFT size=(98304,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 489*2^704557+1 is prime! (-1279.9873s+0.0000s) [Elapsed time: 50.57 minutes] modified 2010-03-13 18:56:31 created 2010-01-31 20:23:02 id 112586