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: ((110048 · 1051000-1)2+1)/2 Verification status (*): Proven Official Comment: Unofficial Comments: This prime has 1 user comment below. Proof-code(s): (*): p97 : Andersen, OpenPFGW Decimal Digits: 102010   (log10 is 102009.78213431) Rank (*): 10241 (digit rank is 1) Entrance Rank (*): 3610 Currently on list? (*): no Submitted: 10/11/2007 19:10:58 CDT Last modified: 10/11/2007 21:47:16 CDT Removed (*): 7/28/2008 17:46:46 CDT Database id: 82532 Status Flags: none Score (*): 39.6155 (normalized score 0.3676)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

Jens Kruse Andersen writes (11 Oct 2007): 

Centered square

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 82532 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/pfgw -o -f -q"((110048*10^51000-1)^2+1)/2" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 34820483 ((110048*10^51000-1)^2+1)/2 has no small factor. [Ellapsed time: 271.186 seconds] modified 2008-01-03 10:54:43 created 2007-10-11 19:22:01 id 94179

field value prime_id 82532 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/pfgw -tc -q"((110048*10^51000-1)^2+1)/2" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing ((110048*10^51000-1)^2+1)/2 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 17 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(49152,20) to FFT(49152,19) Reduced from FFT(49152,19) to FFT(49152,18) Reduced from FFT(49152,18) to FFT(49152,17) Reduced from FFT(49152,17) to FFT(49152,16) 677748 bit request FFT size=(49152,16) Running N-1 test using base 23 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(49152,20) to FFT(49152,19) Reduced from FFT(49152,19) to FFT(49152,18) Reduced from FFT(49152,18) to FFT(49152,17) Reduced from FFT(49152,17) to FFT(49152,16) 677748 bit request FFT size=(49152,16) Running N+1 test using discriminant 43, base 3+sqrt(43) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(49152,20) to FFT(49152,19) Reduced from FFT(49152,19) to FFT(49152,18) Reduced from FFT(49152,18) to FFT(49152,17) Reduced from FFT(49152,17) to FFT(49152,16) 677756 bit request FFT size=(49152,16) Calling N-1 BLS with factored part 50.01% and helper 0.00% (150.03% proof) ((110048*10^51000-1)^2+1)/2 is prime! (-281.1846s+0.0200s) [Elapsed time: 2.40 hours] modified 2008-01-03 10:54:43 created 2007-10-11 19:23:02 id 94180