Problem 7 » 履歴 » リビジョン 4
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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) answer-7
(assert (< 0 num))
(let loop ([current 3] [count 1] [result '(2)]) [prime 2])
(if
(= count num) 10001 count)
result prime
(let ([next (+ current 2)])
(if (prime? current)
(loop next (add1 count) (cons current result)) current)
(loop next count result))))))
(define answer-7
(car (primes 10001))) prime))))))
(printf "7: ~D~%" answer-7)
```