primV(13876)
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(13876) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Lucas primitive part |
| Proof-code(s): (*): | DK : Dubner, Keller, Cruncher |
| Decimal Digits: | 2900 (log10 is 2899.0673980687) |
| Rank (*): | 100319 (digit rank is 2) |
| Entrance Rank (*): | 2553 |
| Currently on list? (*): | no |
| Submitted: | 7/1995 |
| Last modified: | 2/4/2026 08:59:30 UTC |
| Database id: | 29897 |
| Status Flags: | none |
| Score (*): | 28.5939 (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 103
Subcategory: "Lucas primitive part"
(archival tag id 195676, 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 29897 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 1167879589...1568634401 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000000260270218
trial
Running N-1 test using base 13
Generic modular reduction using generic reduction FMA3 FFT length 1K on A 9631-bit number
Running N-1 test using base 19
Generic modular reduction using generic reduction FMA3 FFT length 1K on A 9631-bit number
Running N-1 test using base 29
Generic modular reduction using generic reduction FMA3 FFT length 1K on A 9631-bit number
Running N+1 test using discriminant 37, base 12+sqrt(37)
Generic modular reduction using generic reduction FMA3 FFT length 1K on A 9631-bit number
Calling N-1 BLS with factored part 59.17% and helper 4.69% (182.21% proof)
1167879589...1568634401 is prime! (1.0959s+0.0005s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
11
23
41
67
409
577
919
1223
1597
1733
3467
3469
3571
17351
20809
41641
63443
98837
324097
662771
1110401
1180853
1434497
4202171
6376021
14719741
97382081
101232653
140916701
594273587
878516651
4765843741
6452026727
66265118449
93974346751
106205194357
521511493561
2344355547421
3345860598013
23230657239121
88704249076841
893346576820363
8030487401843243
8568709610527921
25008386631867389
27159850749888907
52117518727310243
55920023657924567
97311259362337169
2349072345221377801
31812858778255556201
3124791659551720658921
34201673799023762317333
61443319601189051182963
470039965023902754923207
12615632641152025840707529
27752129035785622184033593
187832895196379418081359521
658078658277725444483848541
1182222262471587598420874329
5734631399946403978810581541
17562989891922208519776020423
288936610375479300283199495367727543
207466473701356426452671384771995780689986479
3328249394466320052247384127176625642386457243
795954394282744053474161101150396077552743674481
199187460399042526805980487374118125053459971811841
25079508503804840181134205838507586013443419489649668784179
864642661773369783864102222863446175935488557633038098408767685927127
1577321592017158109450513522899099388393094597641506814552471341884857815320857
3029135813077302377712587490764532171725730308330163172507979186958388447438907
27257546467281177721250771247426031098906573974870041998650375674102822433263601
111706553222156057415926458275446344845524650897003434769435357604236054272951672899431
36636383825124560116868205982384404...(97 digits)...55317086862025833274721942540178843
30863692482741536386094142396265183...(104 digits)...75215168792953376485901860114226331
14508810474032379785492507486479991...(128 digits)...86736511184071823706699990383437281
47
1103
2161
2447
23663
78607
97103
124847
14182583
20733943
424621921
4419998369
562627837283291940137654881
5474303442249842401513080472803833316281938081modified 2026-02-04 08:59:30 created 2026-02-04 08:59:20 id 187669
field value prime_id 29897 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 13 Primality testing primV(13876) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 19 Running N-1 test using base 29 Running N+1 test using discriminant 37, base 12+sqrt(37) Calling N-1 BLS with factored part 2.51% and helper 1.07% (8.62% proof) primV(13876) is Fermat and Lucas PRP! (124.260000 seconds) modified 2003-03-25 17:22:47 created 2003-01-07 16:56:50 id 64126
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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