(210501 + 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: | (210501 + 1)/3 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized Lucas number, Wagstaff |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | M : Morain |
| Decimal Digits: | 3161 (log10 is 3160.6388632128) |
| Rank (*): | 96432 (digit rank is 2) |
| Entrance Rank (*): | 2677 |
| Currently on list? (*): | yes |
| Submitted: | 5/1/1996 |
| Last modified: | 3/13/2023 08:14:36 UTC |
| Database id: | 29287 |
| Status Flags: | none |
| Score (*): | 28.8629 (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 109
Subcategory: "Generalized Lucas Number"
(archival tag id 181338, tag last modified 2023-10-24 02:37:13)- Wagstaff (archivable *)
- Prime on list: yes, rank 11
Subcategory: "Wagstaff"
(archival tag id 181339, tag last modified 2023-10-24 02:37:14)
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 29287 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -tc -hhelper.php?id=1100000000004932329 -q"(2^10501+1)/3" 2>&1
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing (2^10501+1)/3 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000000004932329
Running N-1 test using base 2
Running N-1 test using base 3
Running N-1 test using base 7
Running N+1 test using discriminant 17, base 1+sqrt(17)
Calling N-1 BLS with factored part 67.82% and helper 1.13% (204.60% proof)
(2^10501+1)/3 is prime! (1.0631s+0.0002s)
[Elapsed time: 1.00 seconds]
Helper File:
2
3
5
7
11
13
29
31
41
43
61
71
101
113
127
151
211
251
281
331
337
421
601
701
751
1051
1201
1321
1429
1801
2251
3001
4051
4201
5419
6301
7001
7351
8101
10501
14449
21001
28001
29191
39551
52501
63901
86171
96001
100801
106681
110251
122921
152041
268501
304501
558251
664441
1564921
3205651
3775501
7416361
10022251
10567201
13334701
47392381
60018001
60816001
181165951
229668251
791058001
1182468601
90984652501
146919792181
247772800801
259213867501
269089806001
347833278451
1133836730401
66769116536501
168069194932501
1041815865690181
7223591273619001
34010032331525251
129266711542799251
4710883168879506001
47970133603445383501
94291866932171243501
725688486718330087751
2310141222312973778401
5519485418336288303251
19963778429046466946251
535347624791488552837151
90924211718784632332866751
65421109382455481340378766501
743689627597081157353277424901
2430065924693517198550322751963101
4028493980595041855367835954324501
35758633131596900685051378954141001
1038213793447841940908293355871461401
3065581111593982777238141477447662979750101
511937190014372102141784257057292201840312001
325985508875527587669607097222667557116221139090131514801
2139731020464054092520609592459940706818275139793055476751
1606545773279325100753216665442817637284047671432352410624001
217100085701030760532082456157337409031425675860100163555370465949101
14487249719252223428896755006988463...(124 digits)...05629617735073335209377682635445001
12550512193446898967752724977658980...(141 digits)...02685773829394921837307961878154501
57180395185550076273813670673873264...(160 digits)...49240057412005278225084826899525751
25949863075774998579972911102565635...(171 digits)...14139169313083405083018236047737001
17218478943235090126032381158173289...(362 digits)...10626491006221440892838900400128001
362677457
3029385323633
204351583614713modified 2023-03-13 08:14:36 created 2023-03-13 08:14:35 id 181574
field value prime_id 29287 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 (2^10501+1)/3 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N-1 test using base 7 Running N+1 test using discriminant 17, base 1+sqrt(17) Calling N-1 BLS with factored part 6.04% and helper 0.02% (18.15% proof) (2^10501+1)/3 is Fermat and Lucas PRP! (196.610000 seconds) modified 2003-03-25 17:22:57 created 2003-01-04 22:56:25 id 61943
Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
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