primV(13173)
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(13173) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Lucas primitive part |
| Proof-code(s): (*): | DK : Dubner, Keller, Cruncher |
| Decimal Digits: | 1835 (log10 is 1834.727396684) |
| Rank (*): | 111443 (digit rank is 1) |
| Entrance Rank (*): | 4808 |
| Currently on list? (*): | no |
| Submitted: | 7/1995 |
| Last modified: | 2/4/2026 10:12:16 UTC |
| Database id: | 37773 |
| Status Flags: | none |
| Score (*): | 27.1681 (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 121
Subcategory: "Lucas primitive part"
(archival tag id 195694, 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 37773 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 5338222653...5642402601 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000310511395.txt
trial
Running N-1 test using base 13
Generic modular reduction using generic reduction FMA3 FFT length 640 on A 6095-bit number
Running N-1 test using base 29
Generic modular reduction using generic reduction FMA3 FFT length 640 on A 6095-bit number
Running N-1 test using base 31
Generic modular reduction using generic reduction FMA3 FFT length 640 on A 6095-bit number
Running N+1 test using discriminant 47, base 4+sqrt(47)
Generic modular reduction using generic reduction FMA3 FFT length 640 on A 6095-bit number
Calling N-1 BLS with factored part 64.72% and helper 0.02% (194.17% proof)
5338222653...5642402601 is prime! (0.3971s+0.0004s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
7
11
17
19
23
107
487
877
1097
4391
4513
19763
102481
103681
163309
2396941
3983543
6102101
10225307
21291929
21791641
30650981
555003497
620903629
826061911
979676791
3855072511
5883010433
10424083697
14686239709
5600748293801
9428861799143
24848660119363
80256319951861
533975715909289
1902909253647691
6428266374180601
18965717406821831
52471477541626010209
14297347971975757800833
41071004474575750019238941
229140902900747806964016949
5500902230146438151405489047
12842054866056446184519361561
329541040898736809891408309777
7181634929637355776701081412683
594136812257182681897039452124129
1149884364774317448679684799063561
33986746072920049431867434646693841
1839024687217749777838177040573046069859
1281022664310126591636714711138031790311985591
13345777072640252551741515140876418537140353109
65681302014984838931368740317052761650259332806397127
94780156799166973478031801485815764...(90 digits)...93140019523754235177657262375685791
29678888388700787809464159676625547...(151 digits)...16929518898832770980857897685158401
10318603889032458283910585196298662...(168 digits)...40315476300721971085347888446555231modified 2026-02-04 10:12:16 created 2026-02-04 10:12:06 id 187685
field value prime_id 37773 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 5338222653...5642402601 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000310511395.txt
trial
Running N-1 test using base 13
Generic modular reduction using generic reduction FMA3 FFT length 640 on A 6095-bit number
Running N-1 test using base 29
Generic modular reduction using generic reduction FMA3 FFT length 640 on A 6095-bit number
Running N-1 test using base 31
Generic modular reduction using generic reduction FMA3 FFT length 640 on A 6095-bit number
Running N+1 test using discriminant 47, base 4+sqrt(47)
Generic modular reduction using generic reduction FMA3 FFT length 640 on A 6095-bit number
Calling N-1 BLS with factored part 64.72% and helper 0.02% (194.17% proof)
5338222653...5642402601 is prime! (0.4500s+0.0005s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
7
11
17
19
23
107
487
877
1097
4391
4513
19763
102481
103681
163309
2396941
3983543
6102101
10225307
21291929
21791641
30650981
555003497
620903629
826061911
979676791
3855072511
5883010433
10424083697
14686239709
5600748293801
9428861799143
24848660119363
80256319951861
533975715909289
1902909253647691
6428266374180601
18965717406821831
52471477541626010209
14297347971975757800833
41071004474575750019238941
229140902900747806964016949
5500902230146438151405489047
12842054866056446184519361561
329541040898736809891408309777
7181634929637355776701081412683
594136812257182681897039452124129
1149884364774317448679684799063561
33986746072920049431867434646693841
1839024687217749777838177040573046069859
1281022664310126591636714711138031790311985591
13345777072640252551741515140876418537140353109
65681302014984838931368740317052761650259332806397127
94780156799166973478031801485815764...(90 digits)...93140019523754235177657262375685791
29678888388700787809464159676625547...(151 digits)...16929518898832770980857897685158401
10318603889032458283910585196298662...(168 digits)...40315476300721971085347888446555231modified 2026-02-04 10:11:40 created 2026-02-04 10:11:30 id 187684
field value prime_id 37773 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 Error opening file helper Running N-1 test using base 13 Primality testing primV(13173) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 29 Calling Brillhart-Lehmer-Selfridge with factored part 2.56% primV(13173) is PRP! (17.900000 seconds) modified 2003-03-25 17:22:47 created 2003-01-07 05:19:48 id 63891
Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.