2106693 + 253347 + 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: | 2106693 + 253347 + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Gaussian Mersenne norm 32, generalized unique |
| Proof-code(s): (*): | O : Oakes |
| Decimal Digits: | 32118 (log10 is 32117.793327377) |
| Rank (*): | 68494 (digit rank is 1) |
| Entrance Rank (*): | 536 |
| Currently on list? (*): | yes |
| Submitted: | 9/2/2000 22:16:40 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 4033 |
| Status Flags: | none |
| Score (*): | 36.0505 (normalized score 0.0001) |
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.
- Gaussian Mersenne norm (archivable *)
- Prime on list: yes, rank 10
Subcategory: "Gaussian Mersenne norm"
(archival tag id 191165, tag last modified 2023-03-11 15:53:59)- Generalized Unique (archivable *)
- Prime on list: no, rank 1528
Subcategory: "Generalized Unique"
(archival tag id 225579, tag last modified 2024-04-26 18:37:20)
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 4033 person_id 9 machine WinXP Athlon 1.3GHz what prime notes PFGW Version 20021217.Win_Dev (Beta 'caveat utilitor') [FFT v22.7 w/P4] Running N-1 test using base 3 Primality testing 2^106693+2^53347+1 [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 50.00% 2^106693+2^53347+1 is prime! (374.528000 seconds) modified 2003-03-25 17:22:49 created 2003-01-06 19:57:51 id 63677
Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
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