U(12113, - 1, 3499)

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At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important PrimePages database: 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:

Description:	U(12113, - 1, 3499)
Verification status (*):	PRP
Official Comment (*):	Generalized Lucas number
Unofficial Comments:	This prime has 1 user comment below.
Proof-code(s): (*):	CH3 : Broadhurst, Water, OpenPFGW, Primo, CHG
Decimal Digits:	14284 (log₁₀ is 14283.2145172)
Rank (*):	78043 (digit rank is 1)
Entrance Rank (*):	25303
Currently on list? (*):	no
Submitted:	9/24/2005 01:10:45 UTC
Last modified:	3/11/2023 15:54:10 UTC
Database id:	75689
Status Flags:	Verify
Score (*):	33.5445 (normalized score 0)

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 Lucas Number (archivable *)
Prime on list: no, rank 30
Subcategory: "Generalized Lucas Number"
(archival tag id 192585, tag last modified 2023-10-24 02:37:13)

User comments about this prime (disclaimer):

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Chris Caldwell writes (11 Sep 2014): (report abuse)

CHG proof with BLS helper primV(12113,-1,875). For certificate of primality see http://physics.open.ac.uk/~dbroadhu/cert/b3499.zip

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 75689

person_id 9

machine Linux P4 2.8GHz

what prp

notes Command: /home/caldwell/client/pfgw -f -tc -hp75689.txt -q"lucasU(12113,-1,3499)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing lucasU(12113,-1,3499) [N-1/N+1, Brillhart-Lehmer-Selfridge] Reading factors from helper file p75689.txt trial factoring to 4222462 Running N-1 test using base 2 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(6144,21) to FFT(6144,20) Reduced from FFT(6144,20) to FFT(6144,19) Reduced from FFT(6144,19) to FFT(6144,18) Reduced from FFT(6144,18) to FFT(6144,17) Reduced from FFT(6144,17) to FFT(6144,16) 94904 bit request FFT size=(6144,16) Running N+1 test using discriminant 11, base 1+sqrt(11) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(6144,21) to FFT(6144,20) Reduced from FFT(6144,20) to FFT(6144,19) Reduced from FFT(6144,19) to FFT(6144,18) Reduced from FFT(6144,18) to FFT(6144,17) Reduced from FFT(6144,17) to FFT(6144,16) 94912 bit request FFT size=(6144,16) Calling N+1 BLS with factored part 0.64% and helper 0.60% (2.52% proof) lucasU(12113,-1,3499) is Fermat and Lucas PRP! (120.0343s+0.0047s) [Elapsed time: 120 seconds] Helper File: 2 2 43 113 349 373 463 1049 1201 1801 2287 2521 3499 12113 12113 16381 17569 29401 101501 111217 267749 972131 1054201 1541347 4373041 4662197 5679941 7069141 24430001 31439561 105391751 302617501 1386993001 3919952749 16571234749 22145326681 50606739637 71702570801 20235035267501 56945068268251 154346325121451 723491199699449 21528158278277669 142374440616942101 767347423522172921 28401360731618025677 29703769508821403249 88781998068605997733 432152714521920087251 451858091377877133461 14585676742020174948507614196693707 1606520743859528015987800953117194727351901 396838620843257688808286016255332038685954549 90802877487131874454406219904907600026914616091884193349 628788163811319198554215388088859309000803664873230680659130131 9987422208824075232770930401812479148307706514157902533426320762920475016560387 24030595749441757393824407513540588...(193 digits)...83530344652633470999609034634665327 89337153138936176213407439560656705...(2450 digits)...83642640445190688045034381854889001 2 3 5 139 149 317 397 499 587 2099 2333 2437 2801 3673 6997 7001 8269 21499 24499 67339 68539 98473 135469 264899 388099 4008089 16933001 18798253 45582241 48908257 96489997 302484499 591610141 1207529209 12005493499 45804709579 77869001299 10394565816001 241767773855579 524671871138917 33377523399392028053 112085961805604218699 3100029087287401931201 8482427258869136540354801 15296509373751583052017573 71392527808628058200183401 408860385892610715618014441 6762012944046505981319230379 18513829954449502651892273445431976257 4240774545144913974552793241210049616547 46044542959059094126603317373324311122801 12940722014504774381772356482412950767966269 58253073263033945334011209858669974120204318280601

modified 2020-07-07 22:30:43

created 2005-12-30 17:12:47

id 82131

field	value
prime_id	75689
person_id	9
machine	Linux P4 2.8GHz
what	prp
notes	Command: /home/caldwell/client/pfgw -f -tc -hp75689.txt -q"lucasU(12113,-1,3499)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing lucasU(12113,-1,3499) [N-1/N+1, Brillhart-Lehmer-Selfridge] Reading factors from helper file p75689.txt trial factoring to 4222462 Running N-1 test using base 2 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(6144,21) to FFT(6144,20) Reduced from FFT(6144,20) to FFT(6144,19) Reduced from FFT(6144,19) to FFT(6144,18) Reduced from FFT(6144,18) to FFT(6144,17) Reduced from FFT(6144,17) to FFT(6144,16) 94904 bit request FFT size=(6144,16) Running N+1 test using discriminant 11, base 1+sqrt(11) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(6144,21) to FFT(6144,20) Reduced from FFT(6144,20) to FFT(6144,19) Reduced from FFT(6144,19) to FFT(6144,18) Reduced from FFT(6144,18) to FFT(6144,17) Reduced from FFT(6144,17) to FFT(6144,16) 94912 bit request FFT size=(6144,16) Calling N+1 BLS with factored part 0.64% and helper 0.60% (2.52% proof) lucasU(12113,-1,3499) is Fermat and Lucas PRP! (120.0343s+0.0047s) [Elapsed time: 120 seconds] Helper File: 2 2 43 113 349 373 463 1049 1201 1801 2287 2521 3499 12113 12113 16381 17569 29401 101501 111217 267749 972131 1054201 1541347 4373041 4662197 5679941 7069141 24430001 31439561 105391751 302617501 1386993001 3919952749 16571234749 22145326681 50606739637 71702570801 20235035267501 56945068268251 154346325121451 723491199699449 21528158278277669 142374440616942101 767347423522172921 28401360731618025677 29703769508821403249 88781998068605997733 432152714521920087251 451858091377877133461 14585676742020174948507614196693707 1606520743859528015987800953117194727351901 396838620843257688808286016255332038685954549 90802877487131874454406219904907600026914616091884193349 628788163811319198554215388088859309000803664873230680659130131 9987422208824075232770930401812479148307706514157902533426320762920475016560387 24030595749441757393824407513540588...(193 digits)...83530344652633470999609034634665327 89337153138936176213407439560656705...(2450 digits)...83642640445190688045034381854889001 2 3 5 139 149 317 397 499 587 2099 2333 2437 2801 3673 6997 7001 8269 21499 24499 67339 68539 98473 135469 264899 388099 4008089 16933001 18798253 45582241 48908257 96489997 302484499 591610141 1207529209 12005493499 45804709579 77869001299 10394565816001 241767773855579 524671871138917 33377523399392028053 112085961805604218699 3100029087287401931201 8482427258869136540354801 15296509373751583052017573 71392527808628058200183401 408860385892610715618014441 6762012944046505981319230379 18513829954449502651892273445431976257 4240774545144913974552793241210049616547 46044542959059094126603317373324311122801 12940722014504774381772356482412950767966269 58253073263033945334011209858669974120204318280601
modified	2020-07-07 22:30:43
created	2005-12-30 17:12:47
id	82131

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.