U(389, - 390, 2521)
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(389, - 390, 2521) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized Lucas number |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | x25 : Broadhurst, Water, OpenPFGW, Primo |
| Decimal Digits: | 6530 (log10 is 6529.4816975564) |
| Rank (*): | 91789 (digit rank is 2) |
| Entrance Rank (*): | 21290 |
| Currently on list? (*): | no |
| Submitted: | 8/31/2002 20:35:56 UTC |
| Last modified: | 2/4/2026 11:54:20 UTC |
| Database id: | 22024 |
| Status Flags: | none |
| Score (*): | 31.1179 (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 78
Subcategory: "Generalized Lucas Number"
(archival tag id 194808, tag last modified 2025-10-27 15:37:13)
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 22024 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -hhelper_1100000001168098759.txt -q"lucasU(389,-390,2521)" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing lucasU(389,-390,2521) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000001168098759.txt
trial
Running N-1 test using base 3
Generic modular reduction using generic reduction FMA3 FFT length 2K on A 21691-bit number
Running N+1 test using discriminant 7, base 22+sqrt(7)
Generic modular reduction using generic reduction FMA3 FFT length 2K on A 21691-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 32/21692 ERROR: ROUND OFF 0.5>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 7, base 22+sqrt(7)
Generic modular reduction using generic reduction FMA3 FFT length 2560 on A 21691-bit number
Calling N-1 BLS with factored part 33.61% and helper 0.01% (100.85% proof)
lucasU(389,-390,2521) is prime! (4.3612s+0.0003s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
7
11
13
19
29
31
37
41
43
61
71
73
89
101
109
113
127
181
211
271
281
389
421
491
631
701
967
1051
1163
1399
1481
1709
2017
2161
2281
2521
4201
4243
9241
13441
15289
16217
21673
32887
36919
45361
58897
98713
99401
148891
161911
223633
446713
698923
1426553
1897871
2158591
2321509
2371609
3739051
5816021
14936041
29088151
30966517
40604257
46996421
1915342003
3595070221
4282070761
4306332241
6977522161
11923668541
23134257901
47974558321
88506719113
96797792491
224566069309
582042853261
2376934532017
3066655530121
4312947129961
6882264889417
17972349373273
18446453577241
51201524405137
74043851824951
183767093627713
185197036930579
389374652305801
1440365613382981
3518743820319001
22852225847601361
96049035973904077
213993365584755401
2433054161110449421
4246974465002330881
16614090316840722301
17220278225182413181
30879922920118464739
39770649246298777381
182630858916213543151
591424924157500509847
730974945354957399871
355514203737852356878801
1030843107769256706968261
4584064293067908775363287301
8139574449694217609036434121
12381476252050770612317473257901
2099963753836660553822628292961502061
120866750744038602510129266016412871977
193409879291264177872027269280908146921
773889187604314103251023823798056973561
7713172506219223265314773272188874367553
286441914477663136853178457739198139152101
3173455315674815589399673537380901331924348251
13648388357031767156180562609819379035654399266278016377
153302972562745418805388671555703268730012942614720241059319001
1326881365420994690085379381751351808719623933442113886032036974241
32223411128266143656290047388126063261478988288130549811394885552728257
21847256488323547822096570270078886570723777338128499125098431616698468627597747
82047891501890620926980891933763989537632603468238479596542940809964879023134410001
76637088478972230162082472851811386...(112 digits)...11660395343545087349114902748456381
15488149095746533841176651179992165...(113 digits)...36493659465493294897495601126723871
23562216146828867947979591794045577...(125 digits)...62807702459380850925178293139252491
59688912719609855371983061449748340...(236 digits)...09539056961382848254924960359467881modified 2026-02-04 11:54:20 created 2026-02-04 11:54:15 id 187733
field value prime_id 22024 person_id 9 machine Linux PII 200 what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Primality testing 3031779111...7442455242 Running N-1 test using base 3 9667519181...6726342711 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 7, base 22+sqrt(7) Calling N-1 BLS with factored part 2.69% and helper 0.01% (8.10% proof) U(389,-390,2521) is Fermat and Lucas PRP! (609.090000 seconds) modified 2003-03-25 17:22:44 created 2003-01-08 08:17:21 id 64500
Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.