Re: [math-fun] Leyland primes

Keith: "One possibility is that in those cases y^x is much greater than x^y and y is divisible by 10." Indeed, your examples of the 30th and 37th Leyland primes are (x,y) = (357,20) and (471,20) while the 18th and 34th Leyland primes, (81,80) and (237,200), do not exhibit the long string of zeros. I recently conjectured that for d > 11, 10^(d-1) + (d-1)^10 is the smallest (base ten) d-digit Leyland number. After a bit these will exhibit a long string of zeros after the initial 1. Alas, no primes with y = 10 are yet known.