Difference between revisions of "Leyland number"

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===Leyland numbers===
 
===Leyland numbers===
There are <b>{{#expr:{{PAGESINCATEGORY:Leyland prime P|pages}}-2}}</b> numbers: [[:Category:Leyland_prime_P_proven|{{PAGESINCATEGORY:Leyland prime P proven|pages}} proven primes]] and [[:Category:Leyland prime P PRP|{{PAGESINCATEGORY:Leyland prime P PRP|pages}} PRP's]]
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There are <b>{{#expr:{{formatnum:{{PAGESINCATEGORY:Leyland prime P|pages}}|R}}-2}}</b> numbers: [[:Category:Leyland_prime_P_proven|{{PAGESINCATEGORY:Leyland prime P proven|pages}} proven primes]] and [[:Category:Leyland prime P PRP|{{PAGESINCATEGORY:Leyland prime P PRP|pages}} PRP's]]
 
*[[:Category:Leyland prime P|Category]]
 
*[[:Category:Leyland prime P|Category]]
 
*[[Leyland_prime_P_table|Table]]
 
*[[Leyland_prime_P_table|Table]]

Revision as of 21:25, 3 August 2019

A Leyland number is a number that can be expressed in the form [math]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]x^y-y^x[/math].

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 1481 numbers: 291 proven primes and 1,190 PRP's

Leyland numbers second kind

Reservation history

x=20001-40000, y=11-200 completed by Serge Batalov, 2014-05-03
x=15001-20000, y=1001-2000 completed by Serge Batalov, 2014-05-14
x=40001-330000, y=11-17 completed by Serge Batalov, 2014-05-16
x=330001-400000, y=11-17 completed by Serge Batalov, 2014-05-17
x=400001-500000, y=11-17 completed by Serge Batalov, 2014-05-19
x=20001-30000, y=801-1000 reserved by Dylan Delgado, 2019-07-24

Contribution of Leyland numbers

This graph can be found here:

Leyland P contrib.png

References

External links

Number classes
General numbers
Special numbers
Prime numbers