(424179337 - 1)/42416
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: | (424179337 - 1)/42416 |
|---|---|
| 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: | 43203 (log10 is 43202.71297596) |
| Rank (*): | 65808 (digit rank is 1) |
| Entrance Rank (*): | 50603 |
| Currently on list? (*): | no |
| Submitted: | 11/1/2015 06:32:35 UTC |
| Last modified: | 11/22/2024 08:38:47 UTC |
| Database id: | 120509 |
| Status Flags: | none |
| Score (*): | 36.966 (normalized score 0.0002) |
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 24
Subcategory: "Generalized Repunit"
(archival tag id 218121, tag last modified 2025-01-20 23:37:21)
User comments about this prime (disclaimer):
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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 120509 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -hhelper.php?id=1100000000805129521 -q"(42417^9337-1)/42416" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing (42417^9337-1)/42416 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000000805129521
trial
Running N-1 test using base 19
Generic modular reduction using generic reduction AVX-512 FFT length 16K on A 143517-bit number
Running N+1 test using discriminant 71, base 5+sqrt(71)
Generic modular reduction using generic reduction AVX-512 FFT length 16K on A 143517-bit number
Calling N-1 BLS with factored part 33.86% and helper 0.04% (101.62% proof)
(42417^9337-1)/42416 is prime! (142.4046s+0.0004s)
[Elapsed time: 2.42 minutes]
Helper File:
2
3
5
7
13
17
127
167
193
1571
1693
9337
11161
13553
26041
106273
123553
639517
2819473
2833477
3261257
6826081
59794633
193216297
257034901
528142189
1799159473
1820984467
2044696033
4164417277
10633400581
122974648579
131295370249
312315021043
2137248263387
2469411401761
16443159350281
22643588793664609
252468001984379317
9109903674740542981981397
16535917606194954912535814727554464...(14339 digits)...32193419072416676307366122394629313
245121319
55785002369modified 2024-11-22 08:38:47 created 2024-11-22 08:36:22 id 184624
field value prime_id 120509 person_id 9 machine Using: Xeon 4c+4c 3.5GHz what prp notes Command: /home/caldwell/client/pfgw/pfgw64 -tc -q"(42417^9337-1)/42416" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing (42417^9337-1)/42416 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 19 Running N+1 test using discriminant 71, base 5+sqrt(71) Calling N-1 BLS with factored part 0.18% and helper 0.00% (0.54% proof) (42417^9337-1)/42416 is Fermat and Lucas PRP! (157.3114s+0.0010s) [Elapsed time: 2.62 minutes] modified 2020-07-07 22:30:17 created 2015-11-01 07:41:02 id 166138
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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