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"