# (3040612288 + 698989 · (304068192 + 1))2 + 2

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Description: (3040612288 + 698989 · (304068192 + 1))2 + 2 Proven [none] This prime has 1 user comment below. p192 : Broadhurst, Gallot, Proth.exe, OpenPFGW 110174   (log10 is 110173.20753973) 42035 (digit rank is 2) 1166 no 4/17/2006 04:16:09 CDT 7/7/2006 04:39:47 CDT 3/5/2009 23:46:38 CDT 77601 none 39.8527 (normalized score 0.0098)

David Broadhurst writes (11 May 2021):  (report abuse)
 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.
fieldvalue
prime_id77601
person_id9
machineWinXP Pent_M 1.7GHz Laptop
whatprime
notesCommand: 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
modified2020-07-07 17:30:42
created2006-04-18 07:28:36
id84133

fieldvalue
prime_id77601
person_id9
machineGenToo P3 400MHz
whattrial_divided
notesCommand: /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]
modified2020-07-07 17:30:42
created2006-07-07 04:34:32
id84791

Query times: 0.0005 seconds to select prime, 0.0008 seconds to seek comments.