
The nth Prime Page will now find any of the first 2,623,557,157,654,233 primes or
π( x) for x up to 100,000,000,000,000,000.
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:  (30406^{12288} + 698989 · (30406^{8192} + 1))^{2} + 2 
Verification status (*):  Proven 
Official Comment:  
Unofficial Comments:  This prime has 1 user comment below. 
Proofcode(s): (*):  p192 : Gallot, Broadhurst, Proth.exe, OpenPFGW 
Decimal Digits:  110174 (log_{10} is 110173.207539726) 
Rank (*):  35199 (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 0.0207) 

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.
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 N1 test using base 2 Primality testing (30406^12288+698989*(30406^8192+1))^2+2 [N1/N+1, BrillhartLehmerSelfridge] 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 N1 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  20060714 06:27:06 
created  20060418 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  20060714 06:27:04 
created  20060707 04:34:32 
id  84791 

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.
