742478255901 · 240069 + 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: | 742478255901 · 240069 + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Cunningham chain 2nd kind (4p-3) |
| Proof-code(s): (*): | p395 : Angel, Augustin, NewPGen, OpenPFGW |
| Decimal Digits: | 12074 (log10 is 12073.84158) |
| Rank (*): | 81837 (digit rank is 1) |
| Entrance Rank (*): | 69661 |
| Currently on list? (*): | yes |
| Submitted: | 9/9/2016 15:13:17 UTC |
| Last modified: | 5/20/2023 20:59:19 UTC |
| Database id: | 122187 |
| Status Flags: | none |
| Score (*): | 33.024 (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.
- Cunningham Chains (2nd kind) (archivable class *)
- Prime on list: yes, rank 1, weight 42.206707955158
Subcategory: "Cunningham chain 2nd kind (4p-3)"
(archival tag id 218419, tag last modified 2023-03-11 15:53:59)
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 122187 person_id 9 machine Using: Xeon 4c+4c 3.5GHz what prime notes Command: /home/caldwell/client/pfgw/pfgw64 -t -q"742478255901*2^40069+1" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 742478255901*2^40069+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Calling Brillhart-Lehmer-Selfridge with factored part 99.90% 742478255901*2^40069+1 is prime! (0.8238s+0.0002s) [Elapsed time: 1.00 seconds] modified 2020-07-07 22:30:16 created 2016-09-09 15:21:01 id 167826
Query times: 0.0003 seconds to select prime, 0.0003 seconds to seek comments.
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