|| THE MIRANDA SOLUTION
|| This program finds the sum of primes 
|| of a number given as input
|| You must first increase the Miranda heap space 
|| by typing the following at the Miranda prompt
||       /heap 100000000
|| However, after using this program, chnage
|| the heap back to /heap 1000000  otherwise
|| less computationally-intensive programs
|| will take longer to run.

is_prime  n  = True, if #(factors n) = 1
             = False, otherwise

factors n = [x | x <- [1..(sqroot n)]; n mod x = 0]

sqroot n = entier (sqrt n)

two_primes n 
   = [(x,y) | x <- [entier(n/2), (entier(n/2))-1..1];
             y <- [x..n];
	     x + y = n;
             is_prime x; is_prime y]
		       
three_primes n 
   = [(x,y,z) | x <- [entier(n/2), (entier(n/2))-1..1];
               y <- [entier((n-x)/2), (entier ((n-x)/2))-1..x];
	       z <- [y..n];
               x + y + z= n;
               is_prime x; is_prime y; is_prime z]
	       
sum_of_primes n 
      = my_show1 n,                  if is_prime n
      = my_show2((two_primes n)!0),   if (n mod 2 = 0) 
      = my_show3((three_primes n)!0), otherwise
      
my_show1 :: num -> [char]
my_show1 x = show x
my_show2 :: (num,num) -> [char]
my_show2 (x,y) = show x ++ " + " ++ show y
my_show3 :: (num,num,num) -> [char]
my_show3 (x,y,z) = show x ++ " + " ++ show y ++ " + " ++ show z

sp = sum_of_primes

|| try sp 90118         this returns 44987 + 45131
|| also try sp 4565973  this returns 1521991 + 1521991 + 1521991