primV(5, - 6, 6122)
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: | primV(5, - 6, 6122) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized Lucas primitive part |
| Proof-code(s): (*): | x25 : Broadhurst, Water, OpenPFGW, Primo |
| Decimal Digits: | 4763 (log10 is 4762.2737531246) |
| Rank (*): | 95952 (digit rank is 3) |
| Entrance Rank (*): | 23505 |
| Currently on list? (*): | no |
| Submitted: | 11/9/2001 17:48:49 UTC |
| Last modified: | 2/4/2026 11:55:55 UTC |
| Database id: | 26113 |
| Status Flags: | none |
| Score (*): | 30.1378 (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 primitive part (archivable *)
- Prime on list: no, rank 120
Subcategory: "Generalized Lucas primitive part"
(archival tag id 195317, tag last modified 2023-03-11 15:53:59)
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 26113 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -hhelper_1100000000696815840.txt -q"primV(5,-6,6122)" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing primV(5,-6,6122) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000696815840.txt
trial
Running N-1 test using base 2
Generic modular reduction using generic reduction FMA3 FFT length 1536 on A 15826-bit number
Running N+1 test using discriminant 17, base 3+sqrt(17)
Generic modular reduction using generic reduction FMA3 FFT length 1536 on A 15826-bit number
Calling N-1 BLS with factored part 39.86% and helper 0.27% (119.87% proof)
primV(5,-6,6122) is prime! (2.1352s+0.0051s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
7
11
13
19
31
41
43
61
73
97
101
103
137
181
239
241
307
311
409
541
577
613
919
1021
1123
1171
1201
1297
1531
2161
2467
3061
3313
3541
5849
6121
6781
9001
12241
13441
24481
30839
46441
47431
55117
74161
100981
105401
110161
112771
128521
147799
190537
211501
212161
847009
934117
1678321
1785001
1950271
3108961
8715697
12690943
26807981
35540881
262939681
567764641
927037099
980146969
1383638161
2106930961
9757142011
19353635731
20891158391
68754507401
99617785207
120154781611
264840649921
2478750186961
7963466369401
23412002806867
29274753335383
57372656104261
64508161569121
72085651321561
241317924973591
1536052010629489
1888411753890127
24118169444281201
4760317816590150361
5597780112726834061
8289713345361373993
12346985995648844989
185030498420585333101
252026879350662356041
372810476994982432801
592575109627400042641
2244807299700346905001
2472455165563662277393
1199699502336395787186091
2953728137900959095135649
41819674674441587529015061
740797672014674927371043791
846370054558596518376711409
12644443230579801886843521019
51420576374811381403609445473
115394656437025419824224817341
94260123386979283872547675418641
484601490571886903493518015104501
850271719214350502835132764398471
104274404744025432318303059426328481
4067077533669936706351248605374735249
61981850959910422285012731307171469066599
67189948229360689247329776288122926016737
355030358950508128751160010056920422531594797481
1695821269884357626495979547494748586327330181748085193409
21696069504700098127574440534351441357777820752521896522724409406821
504103876389044242580605284072981501250037549130936744429106198676798115841
3993904453552726024260724548432749035473152400993554437020747464348255765281
192947574673366890512032293049056342391614060796043643547834881402185616614713156561
12961781935464901354853808427112526544221444666053340866294089937876531415006047596753
14895818821200292157309324738042821...(100 digits)...53834801330843501956086376253702821
79208359303986000054328486795405452...(111 digits)...23335160303639111457855358205108681
29
219632773571modified 2026-02-04 11:55:55 created 2026-02-04 11:55:49 id 187735
field value prime_id 26113 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 primV(5,-6,6122) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 17, base 3+sqrt(17) Running N+1 test using discriminant 17, base 5+sqrt(17) Calling N-1 BLS with factored part 4.09% and helper 0.03% (12.32% proof) primV(5,-6,6122) is Fermat and Lucas PRP! (497.520000 seconds) modified 2003-03-25 17:22:55 created 2003-01-05 08:01:06 id 62272
Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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