(4449710093 - 1)/44496
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: | (4449710093 - 1)/44496 |
|---|---|
| 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: | 46911 (log10 is 46910.953754221) |
| Rank (*): | 63259 (digit rank is 1) |
| Entrance Rank (*): | 50776 |
| Currently on list? (*): | no |
| Submitted: | 6/1/2016 07:50:10 UTC |
| Last modified: | 11/22/2024 08:43:59 UTC |
| Database id: | 121723 |
| Status Flags: | none |
| Score (*): | 37.2202 (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: no, rank 21
Subcategory: "Generalized Repunit"
(archival tag id 218339, 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 121723 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -hhelper.php?id=1100000000839911509 -q"(44497^10093-1)/44496" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing (44497^10093-1)/44496 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000000839911509
trial
Running N-1 test using base 2
Generic modular reduction using generic reduction AVX-512 FFT length 16K on A 155835-bit number
Running N-1 test using base 11
Generic modular reduction using generic reduction AVX-512 FFT length 16K on A 155835-bit number
Running N+1 test using discriminant 17, base 3+sqrt(17)
Generic modular reduction using generic reduction AVX-512 FFT length 16K on A 155835-bit number
Calling N-1 BLS with factored part 34.45% and helper 0.03% (103.37% proof)
(44497^10093-1)/44496 is prime! (130.4578s+0.0003s)
[Elapsed time: 2.25 minutes]
Helper File:
2
3
5
7
13
19
37
53
59
307
349
523
1103
1129
1171
2089
9397
10093
11833
17053
38861
44497
2149867
3735817
4725667
5967737
6416831
8971789
21088453
57665689
66113041
79674137
218804653
282848359
610083169
689294273
947002657
1041872851
3580803073
8842094839
55064619653
119907178759
267190895042833
87790106686033669
310757887653285789217
14923538515443994252631
1590774714501331191080881
470339632896665578650615337
134920540376886219171018122910949
117582997525513868547488652991272571
12103910975905932935762727718544332...(96 digits)...13329138877144503960440155561394151
37708340599217852027620649539041337...(99 digits)...75470165419994573932240711707721463
94705413298620849457861709905166626...(455 digits)...41824450606274397158903982174462177
60009030174289744859592948128910028...(15098 digits)...96581638323820735304307722464580481
23
103
5591
22999853modified 2024-11-22 08:43:59 created 2024-11-22 08:41:44 id 184625
field value prime_id 121723 person_id 9 machine Using: Xeon (pool) 4c+4c 3.5GHz what prp notes Command: /home/caldwell/clientpool/1/pfgw64 -tc -q"(44497^10093-1)/44496" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing (44497^10093-1)/44496 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N-1 test using base 11 Running N+1 test using discriminant 17, base 3+sqrt(17) Calling N-1 BLS with factored part 0.20% and helper 0.02% (0.63% proof) (44497^10093-1)/44496 is Fermat and Lucas PRP! (212.4029s+0.0012s) [Elapsed time: 3.53 minutes] modified 2020-07-07 22:30:16 created 2016-06-01 07:53:01 id 167361
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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