jagy@phobeusjunior:~/old drive/home/jagy/Cplusplus$ ./factor
 number to be factored ? 35283528

 = 2^3 * 3^2 * 7^2 * 73 * 137
jagy@phobeusjunior:~/old drive/home/jagy/Cplusplus$


string stringify(int x)
 {
   ostringstream o;
   o << x  ;
   return o.str();
 }

string Factored(int i)
{
  string fac;
  fac = " = ";
  int p = 2;
  int temp = i;
  if (temp < 0 )
  {
    temp *= -1;
    fac += " -1 * ";
  }

  if ( 1 == temp) fac += " 1 ";
  if ( temp > 1)
  {
    int primefac = 0;
    while( temp > 1 && p * p <= temp)
    {
      if (temp % p == 0)
      {
        ++primefac;
        if (primefac > 1) fac += " * ";
         fac += stringify( p) ;
        temp /= p;
        int exponent = 1;
        while (temp % p == 0)
        {
          temp /= p;
          ++exponent;
        } // while p is fac
        if ( exponent > 1)
        {
          fac += "^" ;
          fac += stringify( exponent) ;
        }
      }  // if p is factor
      ++p;
    } // while p
    if (temp > 1 && primefac >= 1) fac += " * ";
    if (temp > 1 ) fac += stringify( temp)  ;
  } // temp > 1
  return fac;
} // Factored

def PrimeSieve(curNum, inputNum):
    prime = True
    addSet = set()
    for cp in PrimeSet:
        daPrime, daSkip = cp
        if curNum == daSkip:
            prime = False
            addSet.add((daPrime, daSkip + daPrime))
            if curNum == inputNum:
                inputNumPF_Set.add( daPrime )
    if prime:
        addSet.add((curNum, curNum + curNum))
    PrimeSet.update(addSet)
    return prime

while True:
    inputNum = int(input('Integer to be factored = '))
    PrimeSet = set()
    inputNumPF_Set = set() # will be be populated with the prime factors
#                          # of inpuutNum, For example, for inputNum = 63,
#                          # inputNumPF_Set = {3, 7}
    inputNumPF_Set = set()
    for x in range(2, inputNum + 1):
        isPrime = PrimeSieve(x, inputNum)
    inputNumFZ = set()
    if isPrime:
        inputNumFZ.add( (inputNum, 1) )
    else:
        unfactored = inputNum
        for p in inputNumPF_Set:
            exp = 0
            r = 0
            while r == 0:
                xxfactored, r = divmod(unfactored, p)
                if r == 0:
                    exp = exp + 1
                    unfactored = xxfactored
                else:
                    inputNumFZ.add( (p, exp) )
    print('The prime factorization of', inputNum, 'is given by', inputNumFZ)

Integer to be factored = 24
The prime factorization of 24 is given by {(3, 1), (2, 3)}
Integer to be factored = 63
The prime factorization of 63 is given by {(3, 2), (7, 1)}
Integer to be factored = 156
The prime factorization of 156 is given by {(13, 1), (3, 1), (2, 2)}
Integer to be factored = 72
The prime factorization of 72 is given by {(3, 2), (2, 3)}
Integer to be factored = 10403
The prime factorization of 10403 is given by {(101, 1), (103, 1)}