(212391 + 1)/3
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: | (212391 + 1)/3 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized Lucas number, Wagstaff |
| Proof-code(s): (*): | M : Morain |
| Decimal Digits: | 3730 (log10 is 3729.5855550177) |
| Rank (*): | 94778 (digit rank is 1) |
| Entrance Rank (*): | 1681 |
| Currently on list? (*): | yes |
| Submitted: | 5/1996 |
| Last modified: | 3/13/2023 09:37:23 UTC |
| Database id: | 27688 |
| Status Flags: | none |
| Score (*): | 29.3779 (normalized score 0) |
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 Lucas Number (archivable *)
- Prime on list: no, rank 100
Subcategory: "Generalized Lucas Number"
(archival tag id 181333, tag last modified 2023-10-24 02:37:13)- Wagstaff (archivable *)
- Prime on list: yes, rank 8
Subcategory: "Wagstaff"
(archival tag id 181334, tag last modified 2023-10-24 02:37:14)
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 27688 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -tc -hhelper.php?id=1100000000006488029 -q"(2^12391+1)/3" 2>&1
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing (2^12391+1)/3 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000000006488029
Running N-1 test using base 2
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N-1 BLS with factored part 46.00% and helper 8.34% (146.36% proof)
(2^12391+1)/3 is prime! (0.9950s+0.0002s)
[Elapsed time: 1.00 seconds]
Helper File:
2
3
7
11
31
43
71
127
151
211
281
331
337
827
2833
4721
5419
12391
13099
29191
37171
86171
106681
122921
132751
152041
161071
179951
184081
664441
1564921
5794391
107429561
128818831
224853721
263483263
516266521
549273481
1824726041
2006647231
3812358161
27989941729
873791632531
2354488203481
3203431780337
4453762543897
452824604065751
6363561727426051
78215598439665331
170735974773267443
1898685496465999273
9213624084535989031
2756788662198217256191
4410975230650827973711
21060218021498561334273027818321
34612315434702943134556428791471
6774027833473375976915021445395839
1102272524932426318899113975892645895609
359931645741056789631351742091222797125100809698191524292297
21256743751927370220630952377105576570016395501658460697868351
616118417295048578293181955408006300135730334724584315102344777
10038903777149910946126741017108754570611942191560591325431728188591011
167087803778100685137282215256230683687068949094424492832211188268061451903148929
11763111754911034189958819922265626030162852411746099534272282742979110559598919617
6043930497790503973481076813462520042997083539133970912065745573049492802026928038019
1120555975329453797460758793161622336521020113400670993101603640935259508257738747978899
34685790485740246824716440792348382...(107 digits)...17697592973437487413465343206165441
29293922760297928248078770598052610...(119 digits)...98085451640486701886767775742174681
27996984755296417351513457702586844...(371 digits)...82833679330310986917270058076799921
1907
2731
1115011
6541393
56890289
425796183929
1624700279478894385598779655842584377
3802306738549441324432139091271828121
128064886830166671444802576129115872060027
3388495837466721394368393204672181522815830368604993048084925840555281177
11658823406671259903148376558383270818131012258146392600439520994131344334162924536139modified 2023-03-13 09:37:23 created 2023-03-13 09:37:22 id 181579
field value prime_id 27688 person_id 9 machine Linux PII 200 what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 2 Primality testing (2^12391+1)/3 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N+1 test using discriminant 7, base 1+sqrt(7) Calling N-1 BLS with factored part 2.69% and helper 0.19% (8.28% proof) (2^12391+1)/3 is Fermat and Lucas PRP! (216.150000 seconds) modified 2003-03-25 17:22:56 created 2003-01-05 01:20:00 id 62052
Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.
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