Also, because of the commutative property of addition, the condition x ≥ y is usually added to avoid double-covering the set of Leyland numbers (so we have 1 < y ≤ x).
By November 2012, the largest Leyland number that had been proven to be prime was 51226753 + 67535122 with 25050 digits.
[6] There are many larger known probable primes such as 3147389 + 9314738,[7] but it is hard to prove primality of large Leyland numbers.
Paul Leyland writes on his website: "More recently still, it was realized that numbers of this form are ideal test cases for general purpose primality proving programs.
They have a simple algebraic description but no obvious cyclotomic properties which special purpose algorithms can exploit."