# Project Euler Problem 87

Problem 87 asks us to find how many numbers below 50 million that can be expressed as the sum of a prime square, cube, and fourth power.

By now we are old hands at this type of problem. By caching the exponents of prime numbers and using a set to filter out duplicates, we can find the solution in roughly 4 seconds:

(defn euler-87 [top]
(count
(into
#{}
(let [squares (map #(expt % 2) primes)
cubes   (map #(expt % 3) primes)
quads   (map #(expt % 4) primes)]
(for [i (take-while #(< % top) squares)
j (take-while #(< % (- top i)) cubes)
k (take-while #(< % (- top i j)) quads)
s [(+ i j k)]
:when (< s top)]
s)))))

(time (euler-87 50000000))  ;; "Elapsed time: 3954.751452 msecs"