A Leyland number is an integer of the form xy + yx with 1 < x ≤ y. The first few Leyland numbers are
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 1y + y1.
Leyland numbers that are also prime are listed in A094133. The largest known Leyland number that is also a prime is 26384405 + 44052638.
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- Richard Crandall and Carl Pomerance, Prime Numbers : A Computational Perspective, Springer, 2005