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: 3 · 1000008458192+3 · 1000008454096+1 Verification status (*): Proven Official Comment: Unofficial Comments: This prime has 1 user comment below. Proof-code(s): (*): p97 : Andersen, OpenPFGW Decimal Digits: 65537   (log10 is 65536.507184034) Rank (*): 18789 (digit rank is 2) Entrance Rank (*): 4688 Currently on list? (*): no Submitted: 1/7/2006 21:45:26 CDT Last modified: 1/7/2006 23:21:31 CDT Removed (*): 2/14/2006 06:13:49 CDT Database id: 76705 Status Flags: none Score (*): 38.2517 (normalized score 0.0857)

User comments about this prime (disclaimer):

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Jens Kruse Andersen writes (4 Mar 2006): 

Cuban prime (difference between successive cubes): (x+1)3-x3 for x = 1000008454096.

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 76705 person_id 9 machine Linux P4 2.8GHz what trial_divided notes Command: /home/caldwell/client/pfgw -o -f -q"3*100000845^8192+3*100000845^4096+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 21696196 3*100000845^8192+3*100000845^4096+1 has no small factor. [Elapsed time: 145.374 seconds] modified 2006-01-18 12:45:08 created 2006-01-07 21:52:00 id 82385

field value prime_id 76705 person_id 9 machine Linux P4 2.8GHz what prime notes Command: /home/caldwell/client/pfgw -t -q"3*100000845^8192+3*100000845^4096+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 3*100000845^8192+3*100000845^4096+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(28672,20) to FFT(28672,19) Reduced from FFT(28672,19) to FFT(28672,18) Reduced from FFT(28672,18) to FFT(28672,17) Reduced from FFT(28672,17) to FFT(28672,16) 435424 bit request FFT size=(28672,16) Running N-1 test using base 7 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(28672,20) to FFT(28672,19) Reduced from FFT(28672,19) to FFT(28672,18) Reduced from FFT(28672,18) to FFT(28672,17) Reduced from FFT(28672,17) to FFT(28672,16) 435424 bit request FFT size=(28672,16) Running N-1 test using base 13 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(28672,20) to FFT(28672,19) Reduced from FFT(28672,19) to FFT(28672,18) Reduced from FFT(28672,18) to FFT(28672,17) Reduced from FFT(28672,17) to FFT(28672,16) 435424 bit request FFT size=(28672,16) Running N-1 test using base 17 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(28672,20) to FFT(28672,19) Reduced from FFT(28672,19) to FFT(28672,18) Reduced from FFT(28672,18) to FFT(28672,17) Reduced from FFT(28672,17) to FFT(28672,16) 435424 bit request FFT size=(28672,16) Calling Brillhart-Lehmer-Selfridge with factored part 40.35% 3*100000845^8192+3*100000845^4096+1 is prime! (-1773.7773s+0.0100s) [Elapsed time: 5310 seconds] modified 2006-01-18 12:45:08 created 2006-01-07 21:53:01 id 82386