primV(5048)
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(5048) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Lucas primitive part |
| Proof-code(s): (*): | DK : Dubner, Keller, Cruncher |
| Decimal Digits: | 1054 (log10 is 1053.297510124) |
| Rank (*): | 129435 (digit rank is 40) |
| Entrance Rank (*): | 9411 |
| Currently on list? (*): | no |
| Submitted: | 7/1995 |
| Last modified: | 2/4/2026 10:42:41 UTC |
| Database id: | 54950 |
| Status Flags: | none |
| Score (*): | 25.4344 (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 140
Subcategory: "Lucas primitive part"
(archival tag id 195713, 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 54950 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 1983855902...5185381601 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000003182769.txt
trial
Running N-1 test using base 37
Generic modular reduction using generic reduction FMA3 FFT length 320 on A 3499-bit number
Running N-1 test using base 43
Generic modular reduction using generic reduction FMA3 FFT length 320 on A 3499-bit number
Running N-1 test using base 53
Generic modular reduction using generic reduction FMA3 FFT length 320 on A 3499-bit number
Running N+1 test using discriminant 67, base 14+sqrt(67)
Generic modular reduction using generic reduction FMA3 FFT length 320 on A 3499-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 38/8084 ERROR: ROUND OFF 0.5>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 67, base 14+sqrt(67)
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3499-bit number
Calling N-1 BLS with factored part 100.00% and helper 33.36% (333.45% proof)
1983855902...5185381601 is prime! (0.2515s+0.0003s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
7
11
13
17
19
23
29
31
41
61
71
83
107
157
167
181
211
241
281
421
503
541
631
911
1009
1427
2161
2207
2521
8641
14503
20641
21211
21803
31249
45361
103681
109441
141961
470209
675607
721561
767131
1461601
5924683
9761221
35239681
65740583
764940961
6506859649
8288823481
10783342081
12317523121
14629892449
184715524801
1051224514831
1444606136927
4322424761927
92180471494753
140207234004601
571385160581761
1983000765501001
2632965592186849
13373763765986881
32361122672259149
159224198782659487
456325413062268961
118021448662479038881
120570028745492370271501
13076262780531942679085440491796970310241
18187670330854769931246011952305049586741201
2351318535491978662728427395842752821091282761528783023
6326190212812960577770773501423250646836627929081807841
231900742042861225269632036231770950710877804680654044867543
1538486683044957457804703332422378490845205172402364196823041
4133654065680671131373457884456821479881716851618282242483663
703313603632480636387647534124359814869585429393166324553121265535908861129962052737601
13243568456015855945299430887530831...(130 digits)...73736241484471911059678869788785089
1087
1103
1601
3041
3361
4481
5208481
28002241
1474956001
2207899583
6135922241
10745088481
10749957121
164154312001
23735900452321
429131853662401
115613939510481515041
2852701737604156897270561
25923666709423965629730241
4556600908730770029538033382046792922344961
361833124558013101098932837534321416609222421794081
2624803825209016498351557742768378467155902758505018186043726950561modified 2026-02-04 10:42:41 created 2026-02-04 10:42:31 id 187714
field value prime_id 54950 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 37 Primality testing primV(5048) [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 10.89% primV(5048) is PRP! (4.740000 seconds) modified 2003-03-25 17:22:48 created 2003-01-07 03:34:32 id 63792
Query times: 0.0004 seconds to select prime, 0.0003 seconds to seek comments.
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