(2334015439 - 1)/23339
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: | (2334015439 - 1)/23339 |
|---|---|
| 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: | 67435 (log10 is 67434.740967297) |
| Rank (*): | 56845 (digit rank is 1) |
| Entrance Rank (*): | 48727 |
| Currently on list? (*): | yes |
| Submitted: | 3/5/2020 19:13:09 UTC |
| Last modified: | 11/22/2024 09:04:35 UTC |
| Database id: | 130731 |
| Status Flags: | none |
| Score (*): | 38.3398 (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 10
Subcategory: "Generalized Repunit"
(archival tag id 223916, 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 130731 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -hhelper.php?id=1100000001462051727 -q"(23340^15439-1)/23339" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing (23340^15439-1)/23339 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000001462051727
trial
Running N-1 test using base 2
Generic modular reduction using generic reduction AVX-512 FFT length 24K on A 224014-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 224014-bit number
Calling N-1 BLS with factored part 33.52% and helper 0.02% (100.58% proof)
(23340^15439-1)/23339 is prime! (355.0182s+0.0015s)
[Elapsed time: 5.92 minutes]
Helper File:
2
3
5
7
17
19
167
311
389
499
997
1117
1373
1489
1801
1993
2791
3163
5147
5479
15439
15919
15937
19841
40177
52267
167329
29495047
3480514262077
2688578686807932871
345194966148688317791
11073172381995795763807
1270988549493392455521083
8732322016753893977860621
73450825674355977030069911
137097980848821251472074142661
157951093286963239556313460471
2880729241467110687391353473523
168861352680027960433525687941931
57048816636016956616367230465965233
105128021743876008361272594169890221
154776251510337309389164156635667356979164211
2228426692428524293470964965546023442887348271462174840079421
31367042515068231127188166489124395...(90 digits)...39615414247485227281036300743275227
26334329597716027756855302162285140...(240 digits)...14701169056137937816569292363895267
30342753560285092341933644367689210...(258 digits)...98623035766117094647970966850014693
73714451082731447640019585989989875...(21487 digits)...93792489150851739102273463307244299
83
166613
686731modified 2024-11-22 09:04:35 created 2024-11-22 08:58:40 id 184629
field value prime_id 130731 person_id 9 machine Using: Xeon (pool) 4c+4c 3.5GHz what prp notes Command: /home/caldwell/clientpool/1/pfgw64 -tc -q"(23340^15439-1)/23339" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing (23340^15439-1)/23339 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 11, base 1+sqrt(11) Calling N-1 BLS with factored part 0.12% and helper 0.02% (0.37% proof) (23340^15439-1)/23339 is Fermat and Lucas PRP! (427.9397s+0.0006s) [Elapsed time: 7.13 minutes] modified 2020-07-07 22:30:10 created 2020-03-05 19:16:01 id 176417
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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