(4022521 - 1)/401
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: | (4022521 - 1)/401 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized repunit |
| Proof-code(s): (*): | x4 : Saridis, Curry, Unknown |
| Decimal Digits: | 6563 (log10 is 6562.6507354533) |
| Rank (*): | 88947 (digit rank is 1) |
| Entrance Rank (*): | 15128 |
| Currently on list? (*): | no |
| Submitted: | 11/22/2000 01:27:20 UTC |
| Last modified: | 11/27/2024 07:55:31 UTC |
| Database id: | 21931 |
| Status Flags: | none |
| Score (*): | 31.1337 (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.
- Generalized Repunit (archivable *)
- Prime on list: no, rank 120
Subcategory: "Generalized Repunit"
(archival tag id 194804, tag last modified 2024-09-26 03:37:11)
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 21931 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -hhelper.php?id=1100000000439186843 -q"(402^2521-1)/401" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing (402^2521-1)/401 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000000439186843
trial
Running N-1 test using base 3
Generic modular reduction using generic reduction AVX-512 FFT length 2K on A 21801-bit number
Running N+1 test using discriminant 7, base 16+sqrt(7)
Generic modular reduction using generic reduction AVX-512 FFT length 2K on A 21801-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 37/21906 ERROR: ROUND OFF 0.48911>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 7, base 16+sqrt(7)
Generic modular reduction using generic reduction AVX-512 FFT length 4608 on A 21801-bit number
Calling N-1 BLS with factored part 35.70% and helper 0.28% (107.38% proof)
(402^2521-1)/401 is prime! (4.7096s+0.0002s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
7
11
13
19
29
31
37
41
43
61
67
71
73
109
113
127
181
193
211
241
281
379
409
421
601
631
661
883
991
1009
1051
1171
1289
2381
2521
3769
4933
7057
7547
7561
12421
12841
19391
19471
22051
23029
27253
32321
43633
53353
54151
66361
74161
121631
152767
162007
217981
228859
247591
410257
483481
692371
856381
986437
1194241
1294561
1331821
1957831
2478691
3374521
4347481
6198193
6929077
7212661
18221761
18511921
20260553
24547177
26859211
29232289
33257911
33675461
126354691
164316391
436201921
2629994641
2945259281
4215306841
4439810761
30418544161
138815283713
270480687457
285098846761
294408665029
557831423969
625154137981
1462493431921
2569977711841
5293071485857
59182364026381
67648979006281
231707561932153
350601455776321
358850425783753
421859870665381
2187245779621351
3353530100120593
8640279821640793
11310555146253481
43611502600216741
173507802831893041
305063670558319471
3743328440038729609
4173189574732363711
6136735174455373993
6598297433180304433
6771601042731814591
29142586473613898041
65852715475445036461
94134014360383637161
716308706624827009051
3113502242132822717017
4800503916973831992841
15383999485565946579583
19084098141994164311467
156190357512019623567601
380526767604732565222561
977828549217255114321881
11146168070960514499291063
12826767534295778702726641
4726978356129418382211465661
12299698623631132381474752761
106324915716066234453847877521
36060537640172165590559721558221
219174921665380133200971494874121
2340237053504611790446318518720721
19660155145844842271774007841856851
419914031977162032809550673601119841
750892465531436931962897681184149401
1359741370245482441349575581201742251
837229691508920803144615613829425126698457969
66219313179958569740978503242241714820542665101
752072564985059436660653565027415716061839721441
11519012690005368879976545819830259642942333144271
119069531789875244923735158117661279812336367811941
1791084931312744783985346867623606460610940047349870041
24130699377248116400662801489531376504139665497469721827479068341
42705625478502370172878124943749961104396869530000797390417080543
68060218715459397650081155679211492584930574651437739331836439729353481
296119001593362340604630473713319564541722408790433127615982199286077787
20423292510319109908299793706617661606957961402309138727589566223609804761
13872018772164663710788844180677527...(103 digits)...48898063251516351740588979287699351
59796655827729148452187009845801840...(172 digits)...54127034951239751936521436076082097
2647
52361
1784799473modified 2024-11-27 07:55:31 created 2024-11-27 07:55:26 id 184809
field value prime_id 21931 person_id 9 machine Linux PII 200 what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Primality testing 4474406665...8026790863 Running N-1 test using base 3 3485219271...0997675151 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 7, base 16+sqrt(7) Calling N-1 BLS with factored part 3.65% and helper 0.14% (11.09% proof) (402^2521-1)/401 is Fermat and Lucas PRP! (620.060000 seconds) modified 2003-03-25 17:22:44 created 2003-01-08 08:50:34 id 64509
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.