primV(19148)
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(19148) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Lucas primitive part |
| Proof-code(s): (*): | p12 : Water, OpenPFGW |
| Decimal Digits: | 4001 (log10 is 4000.8502374666) |
| Rank (*): | 97328 (digit rank is 1) |
| Entrance Rank (*): | 21984 |
| Currently on list? (*): | no |
| Submitted: | 4/25/2001 10:02:26 UTC |
| Last modified: | 2/4/2026 12:18:58 UTC |
| Database id: | 27498 |
| Status Flags: | none |
| Score (*): | 29.5962 (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.
- Lucas primitive part (archivable *)
- Prime on list: no, rank 91
Subcategory: "Lucas primitive part"
(archival tag id 195667, tag last modified 2024-10-11 22:37:11)
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 27498 person_id 9 machine Using: Digital Ocean Droplet what prime notes PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 7083329857...2567948321 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000191299735.txt
trial
Running N-1 test using base 11
Generic modular reduction using generic reduction FMA3 FFT length 1280 on A 13291-bit number
Running N-1 test using base 47
Generic modular reduction using generic reduction FMA3 FFT length 1280 on A 13291-bit number
Running N+1 test using discriminant 59, base 2+sqrt(59)
Generic modular reduction using generic reduction FMA3 FFT length 1280 on A 13291-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 10215/20235 ERROR: ROUND OFF 0.5>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 59, base 2+sqrt(59)
Generic modular reduction using generic reduction FMA3 FFT length 1536 on A 13291-bit number
Calling N-1 BLS with factored part 39.29% and helper 14.65% (132.54% proof)
7083329857...2567948321 is prime! (2.5709s+0.0009s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
7
13
17
19
23
29
37
83
107
113
167
211
227
229
281
421
503
683
797
1009
1063
1367
1427
2129
2393
3457
4787
4789
6841
9349
14503
20521
26449
28729
30323
31249
40699
42293
47881
54833
62929
63841
95419
103681
162451
250343
480167
519499
978347
996967
1461601
1617661
2360483
4483163
29134601
35239681
65740583
186313849
212067587
307826903
764940961
1004311729
2576868083
3336915203
7038398989
10694421739
22905724967
460289405267
486077598803
561434197549
2152958650459
3253246620499
3840318083449
4322424761927
186882319815221
351301301942501
571385160581761
1091346396980401
2380192747321703
3921659181245119
6368731219987307
8603290062529471
65494688793368423
129619845347362523
324968740886536921
5741461760879844361
7220339312790438169
135632596951949754809
2608509549583653221689
252171167457207277136719
9937097834862894689463123626943601
50464301883055466112092671023211703
10576896268544841049395058123116357988366103
1059009573400125529504166094598642626708730201
55178337066529867890457879347065097397315177033672963849
509359556421483451770068101495923382461043707085095635591958006289
867797426379958043968754111726556203753942095378535126252231561241871697593889
225345176392644576472046081031051884269743738118739475646190732639430859830972946129
134165642587156910740228608871391655589962996376961241410895850450896589834123016292571
10509238882573877640006342354679552...(133 digits)...18548147824272457277166452678362857
18612603404226292416940704600692110...(235 digits)...26571314230776632438586505138344809
47
1103
325447
340481
386689
446881
1225729
23537807
185686849
10745088481
10749957121
44643701423
562766385967
9742234786927
2206456200865197103
115613939510481515041
1295084949208301179781925363379827503
48117413372195509248992480097331875029761
86388322617796106112871828623225199110711125117607887
1543264591998068763587428525085857166094507770366933120040961
32852458720045254029553107002072988...(92 digits)...24094117191500612310699730285808641
11085784661672161923301569563556691...(163 digits)...36651805834840137114038692644502223modified 2026-02-04 12:18:58 created 2026-02-04 12:18:48 id 187740
field value prime_id 27498 person_id 9 machine Linux PII 200 what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Reading factors from helper file helper Running N-1 test using base 11 Primality testing primV(19148) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 47 Running N+1 test using discriminant 59, base 2+sqrt(59) Calling N-1 BLS with factored part 4.48% and helper 0.68% (14.12% proof) primV(19148) is Fermat and Lucas PRP! (243.510000 seconds) modified 2003-03-25 17:22:46 created 2003-01-07 18:37:14 id 64164
Query times: 0.0003 seconds to select prime, 0.0003 seconds to seek comments.
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