The Sum Of Two Prime Numbers Is 8585. What Is The Product Of These Two Prime Numbers?

The sum of two prime numbers is 85. What is the product of these two prime numbers?

Expert Answers
baxthum8 eNotes educator| Certified Educator

x = prime number

y = prime number

x+y = 85

1, 84 (neither are prime)

2, 83 (both are prime)

3, 82; 4, 81; 5, 80; 6, 79, ... all evens are paired with a possible odd prime therefore both won't be prime because the only prime even is 2.  All evens counting back from 80 are paired with possible odd primes, however the evens are not prime.

The only possibility is the pair of 2 and 83 at which the product of 2 and 83 is 166.