Tuesday, April 12, 2022

Leyland numbers with exactly one million digits

Some three months ago, I suggested on Mathematica Stack Exchange that there are 39542 Leyland numbers with exactly one million decimal digits. On my earlier-this-month blog post, I pointed out that I had created a dictionary of 39556982 Leyland-number (x,y) pairs in order of increasing magnitude, starting with the smallest 1000000-digit L(999999,10). The Leyland number L(x,y) = x^y + y^x, x ≥ y > 1. It's easy to cull from this list the first 39542 entries and I present them now here. The final L(190793,174294) is the entry just prior the appearance of the 1000001-digit L(1000000,10).

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