primV(9356)
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(9356) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Lucas primitive part |
| Proof-code(s): (*): | DK : Dubner, Keller, Cruncher |
| Decimal Digits: | 1955 (log10 is 1954.4432641388) |
| Rank (*): | 111124 (digit rank is 3) |
| Entrance Rank (*): | 4761 |
| Currently on list? (*): | no |
| Submitted: | 7/1995 |
| Last modified: | 2/4/2026 10:10:28 UTC |
| Database id: | 37444 |
| Status Flags: | none |
| Score (*): | 27.3653 (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 118
Subcategory: "Lucas primitive part"
(archival tag id 195691, 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 37444 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 2775007356...9693968801 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000216874699.txt
trial
Running N-1 test using base 7
Generic modular reduction using generic reduction FMA3 FFT length 640 on A 6493-bit number
Running N-1 test using base 47
Generic modular reduction using generic reduction FMA3 FFT length 640 on A 6493-bit number
Running N-1 test using base 53
Generic modular reduction using generic reduction FMA3 FFT length 640 on A 6493-bit number
Running N+1 test using discriminant 83, base 6+sqrt(83)
Generic modular reduction using generic reduction FMA3 FFT length 640 on A 6493-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 6084/8308 ERROR: ROUND OFF 0.5>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 83, base 6+sqrt(83)
Generic modular reduction using generic reduction FMA3 FFT length 768 on A 6493-bit number
Calling N-1 BLS with factored part 81.36% and helper 6.41% (250.52% proof)
2775007356...9693968801 is prime! (0.7530s+0.0004s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
11
13
17
19
23
29
31
41
61
79
103
107
131
181
233
241
281
467
521
541
859
1171
1249
1951
2081
2161
2339
2341
2521
2731
3121
7013
8641
14029
19891
20641
21529
24571
25717
28081
29717
90481
103681
109441
135721
280561
664561
766531
821641
866581
7162963
21183761
26454871
37928281
57089761
102193207
1932300241
2563566721
4328101441
10783342081
12280217041
14736206161
18104700793
39589685693
50187047747
54975368761
2990475029881
13310038759681
668324145163667
1052645985555841
1064730085134101
5836312049326721
13373763765986881
42426476041450801
94491842183551489
1405116525350034901
5210578279869543001
14167898020159929481
88999250837499877681
2551017286913735861521
123944171348849444948627
1966344318693345608565721
504752765667203736366779801
1887280340371359431888764531
103849927693584542320127327909
212661158362558594566110149801
7162955084739436894477556284321
3208055093127916490190490094868044761
21297603745207089290454435276655652707
34550943155046009857395688412902957315281
950911219014256457284486265052714769135355521
536669916513990100454006752158485954313230881362641
624542923122551721493004981706558585672785333365378999981
1543279476449634699608479692367598435286976050460426712893441
48255546832853548234100259286362876...(125 digits)...47795615529751385989319652937092969
71994842501884568903080925762257976...(186 digits)...32971670724916855164940990315544099
14816505174823116876683452754791772...(213 digits)...20455289970984855040656894744713681
7
47
1103
1601
3041
3329
14503
37409
37441
224449
740687
2402401
5208481
34761383
71467343
106513889
309291841
325759201
10749957121
44729401601
53006952961modified 2026-02-04 10:10:28 created 2026-02-04 10:10:18 id 187682
field value prime_id 37444 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 7 Primality testing primV(9356) [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 7.52% primV(9356) is PRP! (14.830000 seconds) modified 2003-03-25 17:22:47 created 2003-01-07 05:28:29 id 63906
Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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