U(25561)
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(25561) |
|---|---|
| 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: | 5342 (log10 is 5341.5835874275) |
| Rank (*): | 91077 (digit rank is 22) |
| Entrance Rank (*): | 20404 |
| Currently on list? (*): | yes |
| Submitted: | 7/7/2001 19:12:21 UTC |
| Last modified: | 3/13/2023 09:36:11 UTC |
| Database id: | 24043 |
| Status Flags: | none |
| Score (*): | 30.4944 (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 10
Subcategory: "Fibonacci Number"
(archival tag id 195035, 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 24043 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -tc -hhelper.php?id=1000000000012275585 -q"U(25561)" 2>&1
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing U(25561) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1000000000012275585
Running N-1 test using base 7
Running N+1 test using discriminant 13, base 6+sqrt(13)
Calling N-1 BLS with factored part 37.03% and helper 17.67% (128.79% proof)
U(25561) is prime! (5.7955s+0.0012s)
[Elapsed time: 6.00 seconds]
Helper File:
2
3
5
11
17
19
31
41
61
107
181
283
541
569
1277
1279
2131
2521
4261
6673
7669
8521
12781
16187
17041
25561
46861
109441
1882921
2820403
9799987
75309701
166668241
202639681
225541441
247612501
290700271
309273161
3422177281
4072864591
9391325429
10783342081
35537616083
46165371073
774939871681
1006118006507
28043471723581
66490765817401
474672373905841
610984151070661
635099565380941
688846502588399
9207609261398081
51925413905202961
148801317528847861
13106980255603741961
15188929154561485261
49258624519847932639
576270785206279010161
3502022122917114957091
3827206988304012167641
49279722643391864192801
9542536701751530860138281
185790722054921374395775013
4854330439365889765803819529
6268355072242853063634547561
43137227648024611864946839441
474509504128267649899203532561
1580497688396606493459505608361
1768711164177156484437536101651
2685461771004078146839512170941
18610830954068221775735052218328871
49350067782373632504773202327603841
6173854848254634668112285518439037305070441
65078506523042229720675394934789343847611361
1449624706503272013500771133991214372168514837586733081
287984332659793300903558886405350768710659583258163123206241
8705930262835869869976471456400132258810352686129850749939277530711
12324966636176048713264320134300611502007494126386028246988832095247429
8853996174522467507283350064621808292949041096316622294281677406409417861
46340031420667058034785254534330664...(91 digits)...73861699016446703314368158433683501
11062406479492487896512633770364093...(100 digits)...97014247446918697766025438966356121
98402624169185819329698144508150772...(135 digits)...50017219080623675307060519594901441
14465376152833660449523517380148996...(151 digits)...13077739409890458855337976001606291
38459066780360053004217344364978488...(247 digits)...18286970686141791941488543222977581
7
23
241
2161
8641
20641
97127
103681
7889521
753829197905761
13373763765986881
63113074623148001
17597037797005226393973299063
89524270498886375346575386561
7901818152782597078036869393681
2408074313985633908017646908824001
113155881311677036562384385175911527
722294854043934542182678842262080957875303
1955228492335595634554243582108027100074802919321601
32165609929722273666211791549816223828923850302972185505601
96380173097634156870914103117172145...(166 digits)...38031090218197946352123717189744801
92576551782905970821566034880683631...(389 digits)...53525745817138682666509942415252561modified 2023-03-13 09:36:11 created 2023-03-13 09:36:05 id 181578
field value prime_id 24043 person_id 9 machine Linux PII 200 what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Primality testing Reading factors from helper file helper Running N-1 test using base 7 4800684175...6845314961 [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 1.48% and helper 0.49% (4.93% proof) U(25561) is Fermat and Lucas PRP! (346.010000 seconds) modified 2003-03-25 17:22:46 created 2003-01-07 22:10:08 id 64193
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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