(5009110357 - 1)/50090
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: | (5009110357 - 1)/50090 |
|---|---|
| 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: | 48671 (log10 is 48670.711481403) |
| Rank (*): | 62795 (digit rank is 1) |
| Entrance Rank (*): | 51084 |
| Currently on list? (*): | yes |
| Submitted: | 11/8/2016 07:40:54 UTC |
| Last modified: | 11/22/2024 08:48:45 UTC |
| Database id: | 122477 |
| Status Flags: | none |
| Score (*): | 37.3339 (normalized score 0.0003) |
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 20
Subcategory: "Generalized Repunit"
(archival tag id 218506, tag last modified 2024-09-26 03:37:11)
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 122477 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -hhelper.php?id=1100000000881058597 -q"(50091^10357-1)/50090" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing (50091^10357-1)/50090 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000000881058597
trial
Running N-1 test using base 5
Generic modular reduction using generic reduction AVX-512 FFT length 16K on A 161681-bit number
Running N+1 test using discriminant 11, base 1+sqrt(11)
Generic modular reduction using generic reduction AVX-512 FFT length 16K on A 161681-bit number
Calling N-1 BLS with factored part 33.61% and helper 0.02% (100.85% proof)
(50091^10357-1)/50090 is prime! (111.4494s+0.0005s)
[Elapsed time: 1.92 minutes]
Helper File:
2
3
7
13
19
31
59
283
1789
3229
5179
5197
10357
25411
269257
414241
2987707
13048561
47927569
62141179
80937361
544124953
1254554141
8477059141
149977948954753
2373433732209817
3840450136447933
11076013108910329081
41344655726877030469
57336990464149755854134928121536763...(16165 digits)...64716309392731048639145414360317649
12728270941modified 2024-11-22 08:48:45 created 2024-11-22 08:46:50 id 184626
field value prime_id 122477 person_id 9 machine Using: Xeon (pool) 4c+4c 3.5GHz what prp notes Command: /home/caldwell/clientpool/1/pfgw64 -tc -q"(50091^10357-1)/50090" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing (50091^10357-1)/50090 [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 0.12% and helper 0.00% (0.36% proof) (50091^10357-1)/50090 is Fermat and Lucas PRP! (180.8895s+0.0879s) [Elapsed time: 3.02 minutes] modified 2020-07-07 22:30:16 created 2016-11-08 07:43:02 id 168117
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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