### Instruction: Three consecutive primes are summed. When the sum is squared, the result is 72,361. What is the largest of the three primes?### Response: I need to find three consecutive primes that add up to a square root of 72,361.
I can use a calculator to find the square root of 72,361, which is 269.
So I need to find three consecutive primes that add up to 269.
I can start by checking some primes around 269/3, which is about 90.
The closest prime to 90 is 89, but 89 + 97 + 101 = 287, which is too big.
So I need to go lower than 89 for the first prime.
The next lower prime is 83, but 83 + 89 + 97 = 269, which is exactly what I want.
So the three consecutive primes are 83, 89, and 97, and the largest of them is 97.