Leyland number

Encyclopedia : L : LE : LEY : Leyland number

A Leyland number is an integer of the form x^y + y^x with 1 < x ≤ y. The first few Leyland numbers are

8, 17, 32, 54, 57, 100, 145, 177, 320, 368, 512, 593, 945, 1124 (sequence in OEIS)

Because of the commutative property of addition, it is not actually required that y be greater than or equal to x, this simply keeps the algorithm from getting bogged down with duplicates. The requirement that x and y both be greater than 1, however, is important, since without it every positive integer would be a Leyland number of the form 1^y + y¹.

Leyland numbers that are also prime are listed in . The largest known Leyland number that is also a prime is 2638⁴⁴⁰⁵ + 4405²⁶³⁸.

References

• Richard Crandall and Carl Pomerance, Prime Numbers : A Computational Perspective, Springer, 2005

 

---

From Wikipedia, the Free Encyclopedia. Original article here. Support Wikipedia by contributing or donating.
All text is available under the terms of the GNU Free Documentation License See Wikipedia Copyrights for details.