Procedure repeatedly-double

Instead take the number of digits in the 14th Fermat number (4933) and double it ten times.
   (define repeatedly-double ; doubles b
     (lambda (b n)           ; n times, n >= 0
       (if (= n 0)
           b     ; not squared at all
           (repeatedly-double (+ b b) (- n 1))))

   > (repeatedly-double 4933 10)  
   5051392                        
So there are approximately 5,051,392 digits in the 24th Fermat number, the first Fermat number whose primality is unknown.