(45201201 - 1)/4519
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: | (45201201 - 1)/4519 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized repunit, APR-CL assisted |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | F2 : Broadhurst, OpenPFGW, Primo, VFYPR |
| Decimal Digits: | 4387 (log10 is 4386.1662178671) |
| Rank (*): | 93819 (digit rank is 1) |
| Entrance Rank (*): | 21365 |
| Currently on list? (*): | no |
| Submitted: | 4/27/2001 07:39:59 UTC |
| Last modified: | 11/27/2024 07:50:31 UTC |
| Database id: | 26792 |
| Status Flags: | none |
| Score (*): | 29.8821 (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.
- APR-CL assisted (tolerated *)
- Prime on list: no, rank 3
Subcategory: "APR-CL assisted"
(archival tag id 195449, tag last modified 2023-03-11 15:53:59)- Generalized Repunit (archivable *)
- Prime on list: no, rank 130
Subcategory: "Generalized Repunit"
(archival tag id 195448, tag last modified 2024-09-26 03:37:11)
User comments about this prime (disclaimer):
User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.
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 26792 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -hhelper.php?id=1100000000439186879 -q"(4520^1201-1)/4519" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing (4520^1201-1)/4519 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000000439186879
trial
Running N-1 test using base 19
Generic modular reduction using generic reduction AVX-512 FFT length 1536 on A 14571-bit number
Running N+1 test using discriminant 43, base 9+sqrt(43)
Generic modular reduction using generic reduction AVX-512 FFT length 1536 on A 14571-bit number
Calling N-1 BLS with factored part 36.79% and helper 0.30% (110.66% proof)
(4520^1201-1)/4519 is prime! (1.1594s+0.0009s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
7
11
13
17
31
37
41
61
101
113
137
151
181
193
241
251
271
401
491
601
701
941
1153
1201
1951
2861
5851
12781
15121
50707
78541
213281
731851
972661
6241621
6381217
6632401
14814901
22039151
27566761
30201601
41654017
53813701
66859061
100238401
107291761
274278721
346917601
569508701
5053169761
7742327041
8526908881
10863266251
16024628161
21505321951
176095100761
375559225441
827726195873
892833909001
1546034532001
5420113910801
7800446552881
24553014362353
90158941101521
417401223729601
904219517928751
10815960994537201
33116977739956601
463904989743584161
4785680468285225801
21808702487177593601
22502768118167636161
37148573986498453681
173520233600810495761
320120623732153699921
12061896056188555599301
61199688313567898850451
36521537487193339020945361
28092380617311739133390534401
2149304553487130779161972635201
13624986825408465825407678547781
246765379414457889096075731167602401
51343381374082615656341376557017357601
986044569577768820060229643594589955401704072001
107063719190535587922686753298072000942216667924688401
30353932007783013246632070546774692160560852220704355840001
287461209162082445143411085605652364026316233407083875955001
5311872250314469613430014135358526971721044341391897699547214254415713469829975601
477768655220435021285519660151539594601202002199016170316421489880987444189360666194481
22236095830370537115713067909770038...(97 digits)...01216121746127208652992069245891041
31718934696960269986827870341366352...(111 digits)...89544238793516882086981318022044301
46532525572940199302225874426808158...(203 digits)...52766441970486101836419913216624321
599
8950073851modified 2024-11-27 07:50:31 created 2024-11-27 07:50:26 id 184807
field value prime_id 26792 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 19 Primality testing (4520^1201-1)/4519 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 43, base 9+sqrt(43) Calling N-1 BLS with factored part 2.25% and helper 0.07% (6.84% proof) (4520^1201-1)/4519 is Fermat and Lucas PRP! (256.680000 seconds) modified 2003-03-25 17:22:55 created 2003-01-05 05:50:46 id 62183
Query times: 0.0003 seconds to select prime, 0.0003 seconds to seek comments.
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