V(35449)
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: | V(35449) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Lucas number |
| Proof-code(s): (*): | p12 : Water, OpenPFGW |
| Decimal Digits: | 7409 (log10 is 7408.4028592215) |
| Rank (*): | 89410 (digit rank is 1) |
| Entrance Rank (*): | 14776 |
| Currently on list? (*): | yes |
| Submitted: | 3/11/2001 15:28:29 UTC |
| Last modified: | 2/4/2026 11:53:40 UTC |
| Database id: | 20343 |
| Status Flags: | none |
| Score (*): | 31.5099 (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.
- Lucas Number (archivable *)
- Prime on list: yes, rank 14
Subcategory: "Lucas Number"
(archival tag id 194604, tag last modified 2023-12-16 03:37:32)
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 20343 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -hhelper_1000000000014285473.txt -q"V(35449)" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing V(35449) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1000000000014285473.txt
trial
Running N-1 test using base 7
Generic modular reduction using generic reduction FMA3 FFT length 2560 on A 24611-bit number
Running N-1 test using base 11
Generic modular reduction using generic reduction FMA3 FFT length 2560 on A 24611-bit number
Running N+1 test using discriminant 17, base 6+sqrt(17)
Generic modular reduction using generic reduction FMA3 FFT length 2560 on A 24611-bit number
Calling N-1 BLS with factored part 32.28% and helper 6.03% (102.88% proof)
V(35449) is prime! (5.7942s+0.0054s)
[Elapsed time: 10.00 seconds]
Helper File:
2
3
5
13
29
83
211
281
421
1427
2953
3001
9283
35449
70901
155717
4433953
22504837
25991941
38490197
63428557
75654893
228680861
800972881
2088501301
4249391501
9320165401
41773163881
64892142701
203183032361
33128448586319
37469942133541
118143291717707
61359873446706227
642626573732791441
80475423858449593021
184266568579364926017301
197730921266711160612551
36302689192832119042589867
20880409040053273740035640229
192347474285460831200493920089
3427786428141438861194643026387
3768695026320506495615952689771
7469755376995709486574809487481
668360360027354504580730486579217
130504869237181082393073724631146963189384763
1280819632152317623645492492119854765613719836542829
599815538819609601660363022036040658354502392526887271059305161
320997165934459054368564270291181600350589476498697300559962501609
357889790372706798776186261711515017835785616532620883072031919704309640305971173
3896944262364468984431989653605889395802956455451592871589240445325974800179030855254151
66051086934862628303193311335986001...(240 digits)...79474928532122931408658998300002351
34289610929840420505186620429612412...(243 digits)...00432968040043828221220818180967589
15431253303787388588646820918191660...(497 digits)...00633403312832083552270251869163079
33907750970294201715391948559591393...(501 digits)...67204797957582563845576095415763873
7
11
23
101
151
167
14503
35447
207029
2105731
6040681
65740583
11806977001
52605885701
11178509879549
7404102316549121
1524504050627526436016974372007
251241837864116522753816479020252350087
275934365532448364720029429031870808020423
309817880943194818668568153423822378397824685648860301
3432649468200884469970732604304328109464408182842795692160672644175701
16989951043091716701569211319449296...(119 digits)...35149200920361936797986595367445447modified 2026-02-04 11:53:40 created 2026-02-04 11:53:30 id 187732
field value prime_id 20343 person_id 9 machine Linux PII 200 what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Primality testing 2528478246...1221068253 Running N-1 test using base 7 5276114048...6480314001 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 11 Running N+1 test using discriminant 17, base 6+sqrt(17) Calling N-1 BLS with factored part 0.63% and helper 0.33% (2.24% proof) V(35449) is Fermat and Lucas PRP! (957.260000 seconds) modified 2003-03-25 17:22:42 created 2003-01-08 20:43:19 id 64644
Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
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