((((16126746690197645878706631574350890570818738690807 · 31# · 15 · 23337 + 19)2 - 1) · 16126746690197645878706631574350890570818738690807 · 31# · 5 · 23329/3 + 146901611060987)2 - 21580083332313498103833414169) · 40389706714951606997880073568 / 377974016181285958115511 + 1
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: | ((((16126746690197645878706631574350890570818738690807 · 31# · 15 · 23337 + 19)2 - 1) · 16126746690197645878706631574350890570818738690807 · 31# · 5 · 23329/3 + 146901611060987)2 - 21580083332313498103833414169) · 40389706714951606997880073568 / 377974016181285958115511 + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | 6-Carmichael factor (6) |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | p44 : Broadhurst, OpenPFGW |
| Decimal Digits: | 6396 (log10 is 6395.6417174232) |
| Rank (*): | 88376 (digit rank is 1) |
| Entrance Rank (*): | 23796 |
| Currently on list? (*): | no |
| Submitted: | 2/21/2003 03:12:05 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 63867 |
| Status Flags: | none |
| Score (*): | 31.0537 (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.
- n-Carmichael factor (tolerated *)
- Prime on list: no, rank 1
Subcategory: "6-Carmichael factor (6)"
(archival tag id 194823, tag last modified 2023-03-11 15:53:59)
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 63867 person_id 9 machine Linux PII 200 what prime notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Reading factors from helper file helper Running N-1 test using base 79 Primality testing ((((122325527*1318346798...4760964641*31#*15*2^3337+19)^2-1)*122325527*1318346798...4760964641*31#*5*2^3329/3+146901611060987)^2-146901611060987^2)*4038970671...7880073568/3779740161...5958115511+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 97 Calling Brillhart-Lehmer-Selfridge with factored part 33.35% ((((122325527*1318346798...4760964641*31#*15*2^3337+19)^2-1)*122325527*1318346798...4760964641*31#*5*2^3329/3+146901611060987)^2-146901611060987^2)*4038970671...7880073568/3779740161...5958115511+1 is prime! (306.830000 seconds) Helper File: // some easily proven primes: 157637 27737273 122325527 1830384350350051 79445360014789443607 1318346798...4760964641 // // and a Primo proof + Cert_Val check for 3325540892...1523915126\ 7694597703...5993315051\ 4262975616...4080823158\ 9253329833...4569399506\ 3630143310...0278144761\ 9382684931...1216523773\ 2416772421...7470374313\ 6703364928...6158762602\ 2836507098...0522668782\ 6199013436...7597043251\ 1994559502...7745997951\ 4433868353...3202444130\ 6596388010...4743779497\ 6749299137...0498424684\ 9048166509...6565186241\ 7162570584...9404271062\ 6552053664...9843451186\ 3682243841...2373813320\ 3750758513...9012439442\ 5285041694...9918693273 // Certificate for this number was FULLY validated! // Total time used to validate certificate: 3mn 35.067s // There were 151 steps in the primality proof modified 2003-03-25 17:21:41 created 2003-02-21 15:13:01 id 68378
Query times: 0.0003 seconds to select prime, 0.0003 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.