(2474115073 - 1)/24740
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: | (2474115073 - 1)/24740 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized repunit |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | p170 : Wu_T, Primo, OpenPFGW |
| Decimal Digits: | 66218 (log10 is 66217.584798744) |
| Rank (*): | 57075 (digit rank is 1) |
| Entrance Rank (*): | 49233 |
| Currently on list? (*): | yes |
| Submitted: | 7/31/2020 22:16:43 UTC |
| Last modified: | 11/22/2024 09:14:43 UTC |
| Database id: | 131044 |
| Status Flags: | none |
| Score (*): | 38.2836 (normalized score 0.0009) |
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: yes, rank 11
Subcategory: "Generalized Repunit"
(archival tag id 224070, 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 131044 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -hhelper.php?id=1100000001554509527 -q"(24741^15073-1)/24740" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing (24741^15073-1)/24740 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000001554509527
trial
Running N-1 test using base 5
Generic modular reduction using generic reduction AVX-512 FFT length 24K on A 219971-bit number
Running N+1 test using discriminant 11, base 1+sqrt(11)
Generic modular reduction using generic reduction AVX-512 FFT length 24K on A 219971-bit number
Calling N-1 BLS with factored part 34.07% and helper 0.01% (102.21% proof)
(24741^15073-1)/24740 is prime! (245.5041s+0.0006s)
[Elapsed time: 4.18 minutes]
Helper File:
2
3
7
13
17
89
97
139
337
641
2749
2753
3769
5309
7537
11393
12401
15073
19417
24793
57649
128113
661009
719689
1047313
1096489
3856549
5234017
9212561
14751721
87441763
171119953
276384481
612141823
3419218849
4876382321
8967628993
21766556881
32062330249
1044800525627
14082424465873
19857545890513
297135067597021
393560773176313
993435769990777
7586765388098257
1129577183155857193
4568208252506202233
140430405733389754777
140655669869785626593
624693803851630940641
788668753508513239409
29225656283367929376128881
7585590248447139368906579223141880417
2393155604808524930844712869949795542721
4153064319381397324611906128908389756251150714275849921
940156574252556847413281164508677292160717334189888727463575119855848001
28333738955747721259576046845451858...(21913 digits)...19311908312149259053786675848753313
83279611modified 2024-11-22 09:14:43 created 2024-11-22 09:10:32 id 184630
field value prime_id 131044 person_id 9 machine Using: Xeon (pool) 4c+4c 3.5GHz what prp notes Command: /home/caldwell/clientpool/1/pfgw64 -tc -q"(24741^15073-1)/24740" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing (24741^15073-1)/24740 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Running N+1 test using discriminant 11, base 1+sqrt(11) Calling N-1 BLS with factored part 0.18% and helper 0.00% (0.53% proof) (24741^15073-1)/24740 is Fermat and Lucas PRP! (420.0020s+0.0098s) [Elapsed time: 7.02 minutes] modified 2021-04-20 22:39:26 created 2020-07-31 22:21:01 id 176732
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.