core.clj

(import (java.util.concurrent.ThreadLocalRandom))

(defn exp [x n]
  (loop [acc 1 n n]
    (if (zero? n) acc
        (recur (* x acc) (dec n)))))

(defn random-bigint [limit]
  (let [bits (.bitLength limit)]
    (loop [result (BigInteger. bits (java.util.concurrent.ThreadLocalRandom/current))]
      (if (< result limit)
        (bigint result)
        (recur (BigInteger. bits (java.util.concurrent.ThreadLocalRandom/current)))))))

(random-bigint (exp 2N 20))