codepad

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; primes n -- list of primes not greater than n in ascending order
(define (primes n) ; assumes n is an integer greater than one
  (let* ((len (quotient (- n 1) 2)) (bits (make-vector len #t)))
    (let loop ((i 0) (p 3) (ps (list 2))) ; sieve of eratosthenes
      (cond ((< n (* p p))
              (do ((i i (+ i 1)) (p p (+ p 2))
                   (ps ps (if (vector-ref bits i) (cons p ps) ps)))
                  ((= i len) (reverse ps))))
            ((vector-ref bits i)
              (do ((j (+ (* 2 i i) (* 6 i) 3) (+ j p)))
                  ((<= len j) (loop (+ i 1) (+ p 2) (cons p ps)))
                (vector-set! bits j #f)))
            (else (loop (+ i 1) (+ p 2) ps))))))

; digits n [b] -- list of digits of n base b, most significant first
(define (digits n . args)
  (let ((b (if (null? args) 10 (car args))))
    (let loop ((n n) (d '()))
      (if (zero? n) d
        (loop (quotient n b) (cons (modulo n b) d))))))

; filter pred? xs -- elements x of xs that satisfy (pred? x)
(define (filter pred? xs)
  (let loop ((xs xs) (ys '()))
    (cond ((null? xs) (reverse ys))
          ((pred? (car xs))
            (loop (cdr xs) (cons (car xs) ys)))
          (else (loop (cdr xs) ys)))))

(display
  (filter
    (lambda (n)
      (= (length
           (filter
             (lambda (d) (= d 3))
             (digits n)))
         4))
    (primes 100000)))

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