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: (3040612288 + 698989 · (304068192 + 1))2 + 2 Verification status (*): Proven Official Comment: Unofficial Comments: This prime has 1 user comment below. Proof-code(s): (*): p192 : Gallot, Broadhurst, Proth.exe, OpenPFGW Decimal Digits: 110174   (log10 is 110173.207539726) Rank (*): 28108 (digit rank is 2) Entrance Rank (*): 1166 Currently on list? (*): no Submitted: 4/17/2006 04:16:09 CDT Last modified: 7/7/2006 04:39:47 CDT Removed (*): 3/5/2009 23:46:38 CDT Database id: 77601 Status Flags: none Score (*): 39.8527 (normalized score 0.0516)

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.

David Broadhurst writes (17 Apr 2006): 

Near-square prime with a BLS proof helped by the smallest GFN-13 that is prime, namely 30406^(2^13)+1, found and proven by Yves Gallot, in February 1999.

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 77601 person_id 9 machine WinXP Pent_M 1.7GHz Laptop what prime notes Command: pfgw.exe -n -tc -hhelp.txt -q"(30406^12288+698989*(30406^8192+1))^2+2" 2>&1 PFGW Version 20030811.Win_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Reading factors from helper file help.txt Running N-1 test using base 2 Primality testing (30406^12288+698989*(30406^8192+1))^2+2 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 5, base 1+sqrt(5) Running N+1 test using discriminant 5, base 2+sqrt(5) Running N+1 test using discriminant 5, base 4+sqrt(5) N+1: (30406^12288+698989*(30406^8192+1))^2+2 302500/365988Calling N-1 BLS with factored part 33.34% and helper 0.01% (100.02% proof) (30406^12288+698989*(30406^8192+1))^2+2 is prime! (83631.4790s+0.1958s) [Elapsed time: 83628 seconds] Helper File: 30406^8192+1 modified 2006-07-14 06:27:06 created 2006-04-18 07:28:36 id 84133

field value prime_id 77601 person_id 9 machine GenToo P3 400MHz what trial_divided notes Command: /home/caldwell/client/pfgw -o -f -q"(30406^12288+698989*(30406^8192+1))^2+2" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 37804219 (30406^12288+698989*(30406^8192+1))^2+2 has no small factor. [Elapsed time: 315.396 seconds] modified 2006-07-14 06:27:04 created 2006-07-07 04:34:32 id 84791