ホーム - Project Euler

Problem 7¶

$10001$st Prime¶

By listing the first six prime numbers: $2, 3, 5, 7, 11$, and $13$, we can see that the $6$th prime is $13$.
What is the $10,001$st prime number?

10001番目の素数¶

素数を小さい方から6つ並べると 2, 3, 5, 7, 11, 13 であり, 6番目の素数は 13 である.
10001 番目の素数を求めよ.

#!r6rs
#!chezscheme

(import (chezscheme))

(define (prime? num)
  (if (even? num)
    #f
    (let ([count (isqrt num)])
      (let loop ([check-num 3])
        (cond
          [(< count check-num) #t]
          [(zero? (mod num check-num)) #f]
          [else (loop (+ check-num 2))])))))

(define (primes num)
  (assert (and (integer? num)
               (exact? num)
               (positive? num)))
  (let loop ([current 3] [count 1] [result '(2)])
    (if (= count num)
      result
      (let ([next (+ current 2)])
        (if (prime? current)
          (loop next (add1 count) (cons current result))
          (loop next count result))))))

(define answer-7
  (car (primes 10001)))

(printf "7: ~D~%" answer-7)