Prime Product

$85$ must equal an odd plus even . The only even prime is $2$ , so that means the other prime must be $85-2=83$ . Therefore, the product is $83*2=166$ .

Python 2.7:

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def prime(n):
    if n <= 1:
        return False
    if n == 2:
        return True
    for test in xrange(2,n/2):
        if n % test == 0:
            return False
    return True
primes = []
for i in xrange(1,85):
    if prime(i):
        primes.append(i)
for m in primes:
    for n in primes:
        if m + n == 85:
            print "Answer:", m*n

The only even prime number is 2 .

since the sum of two prime numbers is 85 (odd) .

Then one of the two prime numbers is even and the other is odd

so the two prime numbers are 2 , 83

Their product = 166

All primes less than $85$ are odd numbers accept $2$ . When $85$ minus an odd number the result is an even number which is not a prime. Therefore, one of the two primes that add up to $85$ must be $2$ and the other $83$ ; and their product $2\times 83 = \boxed{166}$ .