I got “scheme application not a procedure” in the last recursive calling of a function

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You intend to execute two expressions inside the consequent part of the if, but if only allows one expression in the consequent and one in the alternative.

Surrounding both expressions between parenthesis (as you did) won’t work: the resulting expression will be evaluated as a function application of the first expression with the second expression as its argument, producing the error "application: not a procedure; expected a procedure that can be applied to arguments ...", because (time-prime-test n) does not evaluate to a procedure, it evaluates to #<void>.

You can fix the problem by either using a cond:

(define (search-for-primes n m)
  (cond ((< n m)
         (time-prime-test n)
         (search-for-primes (+ n 1) m))
        (else
         (display " calculating stopped. "))))

Or a begin:

(define (search-for-primes n m)
  (if (< n m)
      (begin
        (time-prime-test n)
        (search-for-primes (+ n 1) m))
      (display " calculating stopped. ")))

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