361658262144 + 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: | 361658262144 + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized Fermat |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | p332 : Johnson6, GeneferCUDA, AthGFNSieve, PrimeGrid, OpenPFGW |
| Decimal Digits: | 1457075 (log10 is 1457074.4909093) |
| Rank (*): | 603 (digit rank is 1) |
| Entrance Rank (*): | 24 |
| Currently on list? (*): | yes |
| Submitted: | 11/5/2011 08:39:16 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 102720 |
| Status Flags: | none |
| Score (*): | 47.7877 (normalized score 14.2934) |
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.
- Generalized Fermat (archivable *)
- Prime on list: no, rank 162
Subcategory: "Generalized Fermat"
(archival tag id 213637, tag last modified 2024-11-21 06:37:16)
User comments about this prime (disclaimer):
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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 102720 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 1 361658 262144 1 2>&1 [Elapsed time: 8.522 seconds] modified 2020-07-07 22:30:30 created 2011-11-05 08:48:02 id 135031
field value prime_id 102720 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/pfgw -t -q"361658^262144+1" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 361658^262144+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 53.71% 361658^262144+1 is prime! (347476.7048s+0.1187s) [Elapsed time: 4.02 days] modified 2020-07-07 22:30:30 created 2011-11-05 08:53:01 id 135032
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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