The sum of three different primes is 82. What is the maximum product of these three primes? The reason! Emergency iiiiiiiiiiiiii11

The sum of three different primes is 82. What is the maximum product of these three primes? The reason! Emergency iiiiiiiiiiiiii11

All prime numbers except 2 are odd
If there is no 2 in the three prime numbers, then there must be three odd numbers, and the sum of them must be odd
There must be a prime number 2
The sum of the other two primes = 82 - 2 = 80
In order to maximize the product, we must maximize the product of the two prime numbers, that is to say, the two prime numbers should be as close as possible when the sum is fixed
So these two prime numbers are 80 / 2 - 3 = 37, 80 / 2 + 3 = 43
Product max = 37 * 43 * 2 = 3182