U(5, - 6, 9601)
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(5, - 6, 9601) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized Lucas number |
| Proof-code(s): (*): | x25 : Broadhurst, Water, OpenPFGW, Primo |
| Decimal Digits: | 7471 (log10 is 7470.1850568933) |
| Rank (*): | 89344 (digit rank is 2) |
| Entrance Rank (*): | 17745 |
| Currently on list? (*): | no |
| Submitted: | 10/23/2001 22:12:49 UTC |
| Last modified: | 2/4/2026 11:53:07 UTC |
| Database id: | 20265 |
| Status Flags: | none |
| Score (*): | 31.5356 (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 72
Subcategory: "Generalized Lucas Number"
(archival tag id 194585, tag last modified 2025-10-27 15:37:13)
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 20265 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -hhelper_1100000000487257499.txt -q"lucasU(5,-6,9601)" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing lucasU(5,-6,9601) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000487257499.txt
trial
Running N-1 test using base 3
Generic modular reduction using generic reduction FMA3 FFT length 2560 on A 24819-bit number
Running N+1 test using discriminant 7, base 6+sqrt(7)
Generic modular reduction using generic reduction FMA3 FFT length 2560 on A 24819-bit number
Calling N-1 BLS with factored part 35.79% and helper 0.01% (107.39% proof)
lucasU(5,-6,9601) is prime! (4.9918s+0.0003s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
11
13
17
31
37
41
43
61
97
101
151
181
193
241
311
353
401
601
641
769
1171
1201
1297
1601
1697
2753
3541
4801
5801
5953
6781
8641
9601
13441
16001
17761
55201
62401
74161
82051
82241
98801
122401
145601
168151
224401
295201
343801
1520801
1678321
1950271
4709377
6827521
18198701
21027841
22243201
38149201
40185601
272040961
473896897
573178201
688490113
3696985841
4926056449
6931400449
7239398401
16386144001
31313147521
68754507401
78180664801
79293484801
103352381953
121206120881
2810800069601
420128256499201
621432697463041
886109293550401
918628247364601
3655688315536801
6857766688588801
19854979505843329
447183309836853377
812610713899205201
1743036582663429761
1748016735462726601
2480431288764419201
3445094930226808321
59773386522355896001
592575109627400042641
21463170766480994553601
28753787197056661026689
271041511600591342728451
340800981614130538049401
1006795824867486182291801
15954097282309262360999041
24446522594290613929804801
28398752673271140825020401
523725520509405963876796759201
13744019238016248925287701988601
445813984361506105237664076966721
2347110840158563816028186318246561
4903626466768570999224738379365121
5268698971721637892050105264560801
623565458885624857143366973953113921
2056871500653135843616345033288599993601
86195404170550610979816678826926988566357088801
63340286662973277706162278988150776663495577436161
969468340373808570706508550701726048182646059654014721
185557673493899628393511797753712811510426567803717540350570565651721278179073
15523616333636111545658127482805217176743001452842004397331253391954360606796397740801
40119919145490526125044681765455826...(100 digits)...06154163508637330993511724990136321
21689155962903072717936052135587026...(110 digits)...12627882392683069211732247328988801
13688984144862621094016966556555508...(139 digits)...38076751995982861272324125006250881
13517228421680357222326162260810130...(199 digits)...00521042705911646971603752858327201
12724020131702934786745482117932671...(210 digits)...48611407263981803158160126130347201
64924544834829464105192243420754343...(495 digits)...25335660343773562957508581729176001modified 2026-02-04 11:53:07 created 2026-02-04 11:53:02 id 187731
field value prime_id 20265 person_id 9 machine Linux PII 200 what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Primality testing 1531288049...3718439839 Running N-1 test using base 3 4377806202...7925517751 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 7, base 6+sqrt(7) Calling N-1 BLS with factored part 2.43% and helper 0.01% (7.30% proof) U(5,-6,9601) is Fermat and Lucas PRP! (833.010000 seconds) modified 2003-03-25 17:22:42 created 2003-01-08 21:34:54 id 64659
Query times: 0.0003 seconds to select prime, 0.0003 seconds to seek comments.
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