3428602715439 · 235678 + 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: | 3428602715439 · 235678 + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Consecutive primes arithmetic progression (1,d=6) |
| Proof-code(s): (*): | p408 : Batalov, PolySieve, OpenPFGW |
| Decimal Digits: | 10753 (log10 is 10752.683302464) |
| Rank (*): | 84468 (digit rank is 3) |
| Entrance Rank (*): | 75205 |
| Currently on list? (*): | yes |
| Submitted: | 4/25/2020 01:54:39 UTC |
| Last modified: | 5/20/2023 20:59:19 UTC |
| Database id: | 130857 |
| Status Flags: | none |
| Score (*): | 32.665 (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.
- Consecutive Primes in Arithmetic Progression (archivable class *)
- Prime on list: yes, rank 4
Subcategory: "1/3"
(archival tag id 238581, tag last modified 2025-02-16 14:52:00)- Arithmetic Progressions of Primes (archivable class *)
- Prime on list: no, rank 104
Subcategory: "1/3"
(archival tag id 230246, tag last modified 2025-02-16 14:52:00)
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 130857 person_id 9 machine Using: Xeon (pool) 4c+4c 3.5GHz what prime notes Command: /home/caldwell/clientpool/1/pfgw64 -t -q"3428602715439*2^35678+1" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 3428602715439*2^35678+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Calling Brillhart-Lehmer-Selfridge with factored part 99.89% 3428602715439*2^35678+1 is prime! (0.5647s+0.0001s) [Elapsed time: 0.00 seconds] modified 2020-07-07 22:30:10 created 2020-04-25 01:56:08 id 176544
Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.