289 · 218502 + 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.
|Description:||289 · 218502 + 1|
|Verification status (*):||Proven|
|Official Comment (*):||Cullen, generalized Fermat|
|Proof-code(s): (*):||K : Keller|
|Decimal Digits:||5573 (log10 is 5572.1178776177)|
|Rank (*):||85769 (digit rank is 1)|
|Entrance Rank (*):||7|
|Currently on list? (*):||short|
|Score (*):||30.6257 (normalized score 0)|
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.
- Cullen primes (archivable *)
- Prime on list: yes, rank 11
Subcategory: "Cullen primes"
(archival tag id 194999, tag last modified 2009-08-04 21:58:38)
- Generalized Fermat (archivable *)
- Prime on list: no, rank 6409
Subcategory: "Generalized Fermat"
(archival tag id 208628, tag last modified 2022-05-20 11:50:23)
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 23436 person_id 9 machine Linux PII 200 what prime notes PFGW Version 1.1 for Pentium and compatibles Running N-1 test using base 3 Primality testing 289*2^18502+1 [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 99.96% 289*2^18502+1 is prime! (35.000000 seconds) modified 2003-03-25 11:26:07 created 2002-12-08 07:55:47 id 29408