(42550837315 · (2110503 - 1) + 1) · 2110505 + 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: | (42550837315 · (2110503 - 1) + 1) · 2110505 + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Consecutive primes arithmetic progression (2,d=4) |
| Proof-code(s): (*): | p408 : Batalov, PolySieve, OpenPFGW |
| Decimal Digits: | 66541 (log10 is 66540.666189816) |
| Rank (*): | 56454 (digit rank is 5) |
| Entrance Rank (*): | 56427 |
| Currently on list? (*): | yes |
| Submitted: | 11/6/2024 17:37:01 UTC |
| Last modified: | 11/7/2024 06:37:16 UTC |
| Database id: | 138706 |
| Status Flags: | none |
| Score (*): | 38.2986 (normalized score 0.001) |
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: "Consecutive primes in arithmetic progression (2,d=*)"
(archival tag id 229731, tag last modified 2024-11-23 01:37:11)- Arithmetic Progressions of Primes (archivable class *)
- Prime on list: no, rank 32
Subcategory: "Arithmetic progression (2,d=*)"
(archival tag id 229732, tag last modified 2024-11-23 01:37:11)
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 138706 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -t -q"(42550837315*(2^110503-1)+1)*2^110505+1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing (42550837315*(2^110503-1)+1)*2^110505+1 [N-1, Brillhart-Lehmer-Selfridge]
trial
Running N-1 test using base 3
Generic modular reduction using generic reduction AVX-512 FFT length 24K on A 221045-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 49.99%
(42550837315*(2^110503-1)+1)*2^110505+1 is prime! (49.3014s+0.0004s)
[Elapsed time: 50.00 seconds]modified 2024-11-07 05:43:51 created 2024-11-07 05:43:01 id 184552
Query times: 0.0003 seconds to select prime, 0.0003 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.