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Leyland number
A Leyland number is a number that can be expressed in the form [math]\displaystyle{ x^y+y^x }[/math], where x and y are positive integers with the condition 1 < x ≤ y. These numbers are named after Paul Leyland, who first studied these numbers in 1994. The first few nontrivial Leyland numbers are given by OEIS sequence A076980.
A Leyland prime is a Leyland number which is also a prime (see sequence A094133 in OEIS).
The second kind of numbers are of the form [math]\displaystyle{ x^y-y^x }[/math].
Contents
History
Data
The data tables contains for every number the x and y values, the number of digits, the Leyland number[1], dates and persons of finding and prooving if available and the program used to proove a prime.
Leyland numbers
There are Expression error: Unrecognized punctuation character ",". numbers: 307 proven primes and 1,507 PRP's
Leyland numbers second kind
Reservation history
Contribution of Leyland numbers
This graph can be found here:
References
External links
- Leyland number
- Main thread of XYYXF Project at MersenneForum
- Current search for Leyland PRP's at MersenneForum
- Prime proofs of Leyland numbers at MersenneForum
- Homepage of Paul Leyland
- Page of Leyland numbers, dated 2006-10-06 by P.Leyland
- Homepage of Andrey Kulsha, dated 2017-01-04
- Yahoo group, 2005 to 2016
- sequence A061119 in OEIS of n^2 + 2^n
- sequence A253471 in OEIS of n^3 + 3^n
- YouTube "Leyland Numbers - Numberphile"
