U(14431)
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(14431) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Fibonacci number |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | p54 : Broadhurst, Water, OpenPFGW |
| Decimal Digits: | 3016 (log10 is 3015.5511514453) |
| Rank (*): | 96383 (digit rank is 4) |
| Entrance Rank (*): | 23804 |
| Currently on list? (*): | short |
| Submitted: | 4/17/2001 18:43:30 UTC |
| Last modified: | 3/13/2023 08:07:12 UTC |
| Database id: | 29537 |
| Status Flags: | none |
| Score (*): | 28.7166 (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.
- Fibonacci Number (archivable *)
- Prime on list: yes, rank 11
Subcategory: "Fibonacci Number"
(archival tag id 179783, tag last modified 2023-09-15 17:37:10)
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 29537 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -tc -hhelper.php?id=1000000000012264455 -q"U(14431)" 2>&1
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing U(14431) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1000000000012264455
Running N-1 test using base 2
Running N+1 test using discriminant 13, base 6+sqrt(13)
Calling N-1 BLS with factored part 47.98% and helper 36.21% (180.15% proof)
U(14431) is prime! (2.1115s+0.0011s)
[Elapsed time: 2.00 seconds]
Helper File:
2
3
7
11
31
43
47
79
89
131
163
199
263
307
521
859
881
967
1951
2081
2731
2789
3331
3607
4441
14431
21649
24571
59369
146521
202049
678211
800483
855997
866581
928157
1121101
1861471
4274579
4935061
37928281
54018521
62043169
93058241
229711171
350207569
370248451
562418561
11445832711
23515719083
42567967201
76984462699
1241763935281
7878454669361
265272771839851
1937097591773821
2918000731816531
6856961839926808711
718487536914797401487
15549579808009384473181
584141201630501365750381
1027729298220237292846693
2304779807964154941798691
306473410026144568738331639521
2012542683746769682376344555951
5690484979405478934633378760841
2684571411430027028247905903965201
498499689898194420244809172257094881821
1101057804780496107528145654405532428291
364870119831435547923863289533519375453761
666146992336447094037882680026427177876016818933
2704719196143346692298887124435589105513805538379
925472857790644020915914940287693742592189563722435401
17732745322135163936648351820424253379372467026985685021596123
7513601265751126919260420528205646210878820214173976884762475096801
56909671435221082533169582520085662884377962564222829999842181652894123123019
11072221460868842712840886447631237814311992880731232108531118674475942575327786544322951
19664644211826977261258200244938258...(92 digits)...69016674440337439189171248007621961
13279921144125924337835703378293223...(96 digits)...95937240904636278719643214169440511
20008667987598526078272251989042096...(121 digits)...59928349231903257545488617686760081
5
61
73
149
233
1409
2207
2221
6733
80809
135721
779329
1317941
1529581
24534401
40719241
120542449
278574997
14736206161
1582841707201
5877820495007
6086461133983
17082086114207
35214687873301
49649320649221
1459000305513721
319702847642258783
2992628320901882161
88999250837499877681
196447231496394995461
449926462154679532703
2728696087948303670341
1702945513191305556907097618161
2636702406716842490558409218497729
13508599996297878561172632097269367885776721
77793983007494113730299744096232053147887131423
183707757246801094558768264908628886377124291177
7234132139647167989475582370803952487649173808170830204282463
923491964053979620044267467977143148287651427604351735846749847194791541
15690986647773496661603303755935902...(121 digits)...56434714549433177395658290683120673
27403892693704344624236559749023658...(334 digits)...57719733129319712013423543105689401modified 2023-03-13 08:07:12 created 2023-03-13 08:07:10 id 181573
field value prime_id 29537 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 2 Primality testing U(14431) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 13, base 6+sqrt(13) Calling N-1 BLS with factored part 3.07% and helper 1.28% (10.52% proof) U(14431) is Fermat and Lucas PRP! (120.580000 seconds) modified 2003-03-25 17:22:57 created 2003-01-04 21:49:40 id 61879
Query times: 0.0038 seconds to select prime, 0.0004 seconds to seek comments.
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