(42241009 - 1)/4223
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: | (42241009 - 1)/4223 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized repunit |
| Proof-code(s): (*): | x14 : Steward, OpenPFGW, Primo |
| Decimal Digits: | 3655 (log10 is 3654.7298036301) |
| Rank (*): | 94917 (digit rank is 1) |
| Entrance Rank (*): | 20548 |
| Currently on list? (*): | no |
| Submitted: | 11/19/2000 12:34:00 UTC |
| Last modified: | 11/28/2024 04:25:54 UTC |
| Database id: | 27825 |
| Status Flags: | none |
| Score (*): | 29.3148 (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 138
Subcategory: "Generalized Repunit"
(archival tag id 186203, 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 27825 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -hhelper.php?id=1100000000439186906 -q"(4224^1009-1)/4223" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing (4224^1009-1)/4223 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000000439186906
trial
Running N-1 test using base 23
Generic modular reduction using generic reduction AVX-512 FFT length 1536 on A 12141-bit number
Running N+1 test using discriminant 31, base 10+sqrt(31)
Generic modular reduction using generic reduction AVX-512 FFT length 1536 on A 12141-bit number
Calling N-1 BLS with factored part 34.13% and helper 0.01% (102.39% proof)
(4224^1009-1)/4223 is prime! (0.9688s+0.0010s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
7
11
13
17
19
29
37
43
73
97
109
113
127
181
197
337
457
659
757
1009
1153
2017
2437
2731
3529
4789
6449
7489
13033
15121
17333
28001
35267
38561
71569
124153
258721
616393
1296833
1705141
2548279
3377161
4906273
10583497
11553193
16645693
17846401
29588329
76261249
86891477
169031497
293655937
1115955611
1487171449
1501294369
1582373801
1859078929
3171108529
4410128647
11222587921
19930354417
90207771769
166918691143
235296015529
256521550697
388468378729
403837296913
482959769489
1700132886901
1617777120691621
3155248279972433
115378633754830097
11110068458529172609
52109506377868380517
298944010280967588379
917818021329804349921
1613899231986798924604849
26014091425959030193575637
1308113803623180156804108559
3532869563774508962427269089
57394033536140680248443997529
9213760498545241375815924309200881
1400147008850682755154759318382477777
36298439695189579583756187573585260833609
2873217549886377456598011499649465376183863953
227108881862890529563959933342420187054408387513
29747896815730850494610356534250121922701434530273
14137967779247945235284975615699646363693151722278497
401416448154084952083270854669497822952564618171260271737
521899877721920965166721253559052414245425017784696774297
14588891334279945747799821502549935967944606129862164336895705039
12434750714049597735328408029208264...(105 digits)...53640123676125943478967723400325867modified 2024-11-28 04:25:54 created 2024-11-28 04:25:49 id 184810
field value prime_id 27825 person_id 9 machine Linux PII 200 what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 23 Primality testing (4224^1009-1)/4223 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 31, base 10+sqrt(31) Calling N-1 BLS with factored part 3.32% and helper 0.01% (9.98% proof) (4224^1009-1)/4223 is Fermat and Lucas PRP! (170.400000 seconds) modified 2003-03-25 17:22:56 created 2003-01-05 01:02:20 id 62045
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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