Project Euler

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# [[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.

```scheme

#!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)

```