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 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: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 : Water, Broadhurst, Primo, OpenPFGW, CHG
Decimal Digits:14284   (log10 is 14283.2145172)
Rank (*):68206 (digit rank is 1)
Entrance Rank (*):25303
Currently on list? (*):short
Submitted:9/23/2005 20:10:45 CDT
Last modified:12/30/2005 11:14:47 CDT
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: yes, rank 15
Subcategory: "Generalized Lucas Number"
(archival tag id 192585, tag last modified 2016-05-02 05:50:25)

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.

Chris Caldwell writes (11 Sep 2014): 
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.
fieldvalue
prime_id75689
person_id9
machineLinux P4 2.8GHz
whatprp
notesCommand: /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
modified2005-12-30 11:16:04
created2005-12-30 11:12:47
id82131

Query times: 0.0004 seconds to select prime, 0.0003 seconds to seek comments.