To find the product of two prime numbers whose sum is 85, let’s first identify those prime numbers.
The sum of two prime numbers, say p1 and p2, is given by:
- p1 + p2 = 85
By analyzing the primes less than 85, we find pairs of primes that add up to 85. Notably, one of the prime numbers must be even. The only even prime number is 2. Thus, we can calculate the other prime:
- p1 = 2, p2 = 85 – 2 = 83
Next, we check if both 2 and 83 are prime numbers:
- 2 is prime.
- 83 is also prime (it has no divisors other than 1 and 83).
Now that we have found our two prime numbers, 2 and 83, we can calculate their product:
- Product = p1 × p2 = 2 × 83 = 166
Therefore, the product of the two prime numbers whose sum is 85 is 166.