V(12251)

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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:	V(12251)
Verification status (*):	Proven
Official Comment (*):	Lucas number
Unofficial Comments:	This prime has 1 user comment below.
Proof-code(s): (*):	p54 : Broadhurst, Water, OpenPFGW
Decimal Digits:	2561 (log₁₀ is 2560.3075807025)
Rank (*):	97755 (digit rank is 2)
Entrance Rank (*):	25353
Currently on list? (*):	short
Submitted:	5/13/2001 12:38:58 UTC
Last modified:	3/13/2023 06:43:19 UTC
Database id:	30846
Status Flags:	none
Score (*):	28.2069 (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.

Lucas Number (archivable *)
Prime on list: yes, rank 18
Subcategory: "Lucas Number"
(archival tag id 179786, tag last modified 2023-12-16 03:37:32)

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 (11 Sep 2014): (report abuse)

notes

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 30846

person_id 9

machine Using: Digital Ocean Droplet

what prime

notes Command: /var/www/clientpool/1/pfgw64 -tc -hhelper.php?id=1000000000014262275 -q"V(12251)" 2>&1
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing V(12251) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1000000000014262275
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 1+sqrt(11)
Running N+1 test using discriminant 11, base 2+sqrt(11)
Calling N+1 BLS with factored part 50.99% and helper 16.34% (169.34% proof)

V(12251) is prime! (1.7369s+0.0011s)
[Elapsed time: 1.00 seconds]

Helper File:
2
3
11
29
71
101
151
251
491
911
1471
12251
54601
85751
560701
2440201
7517651
9503467
51636551
88972241
112128001
149401001
352175251
599786069
1056945751
4353947431
15228911251
28143378001
459807660691
3792283747547
10282952391251
31550609385723751
95321634893269751
3774666296736155101
5971841400862716751
6280626287929792751
10674487697887361640251
4326644238167324920156419143057466978443914837739641651
557778681056845466177714798959180644951277797573934513902763152301
5
13
97
701
3001
14293
30631
141961
990371
1337701
1695401
6168709
5121507529
424543452901
3242370312301
1368231730520598301
158414167964045700001
17231203730201189308301
701022476795100220064501
303428489268486159678418501
205286717066010830378001643001
105878242849662766254646765594362401
128955073914024460192651484843195641
104489406798697025053110107015655603906769001
7788530618790666624432955667494630820914012206703787501
78385399869327423334596543897285705191182320444657944726519698324612539594187884222001
38904179238223053326519747808323857...(825 digits)...83947870771925959476329428081817501

modified 2023-03-13 06:43:19

created 2023-03-13 06:43:17

id 181562

field	value
prime_id	30846
person_id	9
machine	Using: Digital Ocean Droplet
what	prime
notes	Command: /var/www/clientpool/1/pfgw64 -tc -hhelper.php?id=1000000000014262275 -q"V(12251)" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing V(12251) [N-1/N+1, Brillhart-Lehmer-Selfridge] Reading factors from helper file helper.php?id=1000000000014262275 Running N-1 test using base 3 Running N+1 test using discriminant 11, base 1+sqrt(11) Running N+1 test using discriminant 11, base 2+sqrt(11) Calling N+1 BLS with factored part 50.99% and helper 16.34% (169.34% proof) V(12251) is prime! (1.7369s+0.0011s) [Elapsed time: 1.00 seconds] Helper File: 2 3 11 29 71 101 151 251 491 911 1471 12251 54601 85751 560701 2440201 7517651 9503467 51636551 88972241 112128001 149401001 352175251 599786069 1056945751 4353947431 15228911251 28143378001 459807660691 3792283747547 10282952391251 31550609385723751 95321634893269751 3774666296736155101 5971841400862716751 6280626287929792751 10674487697887361640251 4326644238167324920156419143057466978443914837739641651 557778681056845466177714798959180644951277797573934513902763152301 5 13 97 701 3001 14293 30631 141961 990371 1337701 1695401 6168709 5121507529 424543452901 3242370312301 1368231730520598301 158414167964045700001 17231203730201189308301 701022476795100220064501 303428489268486159678418501 205286717066010830378001643001 105878242849662766254646765594362401 128955073914024460192651484843195641 104489406798697025053110107015655603906769001 7788530618790666624432955667494630820914012206703787501 78385399869327423334596543897285705191182320444657944726519698324612539594187884222001 38904179238223053326519747808323857...(825 digits)...83947870771925959476329428081817501
modified	2023-03-13 06:43:19
created	2023-03-13 06:43:17
id	181562

field value

prime_id 30846

person_id 9

machine Linux PII 200

what prp

notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 3 Primality testing V(12251) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 11, base 1+sqrt(11) Calling N-1 BLS with factored part 1.58% and helper 1.05% (5.80% proof) V(12251) is Fermat and Lucas PRP! (69.820000 seconds)

modified 2003-03-25 17:22:58

created 2003-01-04 20:03:31

id 61747

field	value
prime_id	30846
person_id	9
machine	Linux PII 200
what	prp
notes	PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 3 Primality testing V(12251) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 11, base 1+sqrt(11) Calling N-1 BLS with factored part 1.58% and helper 1.05% (5.80% proof) V(12251) is Fermat and Lucas PRP! (69.820000 seconds)
modified	2003-03-25 17:22:58
created	2003-01-04 20:03:31
id	61747

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