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: (110314177-1)/11030 Verification status (*): Proven Official Comment: Generalized repunit Unofficial Comments: This prime has 1 user comment below. Proof-code(s): (*): p54 : Water, Broadhurst, OpenPFGW Decimal Digits: 16882   (log10 is 16881.9597974138) Rank (*): 37633 (digit rank is 1) Entrance Rank (*): 21193 Currently on list? (*): short Submitted: 2/23/2005 16:32:23 CDT Last modified: 1/18/2007 14:01:49 CDT Database id: 73519 Status Flags: none Score (*): 34.0619 (normalized score 0.0014)

Archival tags:

There are certain forms classed as archivable: these prime may (at times) remain on this list even if they do not make the Top 5000 proper.  Such primes are tracked with archival tags.

Generalized Repunit (archivable *)

Prime on list: yes, rank 14
Subcategory: "Generalized Repunit"
(archival tag id 192414, tag last modified 2009-07-12 03:50:27)

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 (4 Jan 2007): 

Note: BLS proof with BLS helper

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 73519 person_id 9 machine WinXP Pent_M 1.7GHz Laptop what prime notes Command: pfgw.exe -n -tc -hhelp.txt -q"(11031^4177-1)/11030" 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 5 Primality testing (11031^4177-1)/11030 [N-1/N+1, Brillhart-Lehmer-Selfridge] Calling N-1 BLS with factored part 37.29% and helper 0.02% (111.89% proof) (11031^4177-1)/11030 is prime! (492.1318s+0.0526s) Running N+1 test using discriminant 11, base 1+sqrt(11) [Elapsed time: 493 seconds] Helper File: 2 2 2 2 2 2 3 7 13 17 19 31 37 59 73 97 163 197 233 349 379 397 433 523 1153 1217 2089 2137 2953 3061 3313 3677 4177 8353 10267 18793 49993 57073 83449 87739 94201 249749 370009 405073 564457 974401 1450871 2963273 3924901 60680413 93478369 124432621 146963321 189120601 956494009 1391290057 4017834001 7418772577 12090956797 419296968757 543967900921 2290380153769 34084531254493 395976968493217 549899662416257 2055104421910849 6280997909294657 12265535475339301 62360391152616457 188599823267613073 20424595446629212177 26049766528361415761 29165034409701972283 650289513823447032013 1976245813202186867976957043153 7341347042645539181284116874369 20601359463800686525446214039992769 99459207194414232453752376974926568...(92 digits)...63490440064102865241064765867444697 87530442922038640816157566173736451...(198 digits)...26671394768419788437392663071820509 18810696958772799426458546064223994...(5434 digits)...96939197478815779498690752406498561 modified 2007-03-03 21:00:42 created 2007-01-18 13:53:35 id 87526