Three consecutive primes are summed. When the sum is squared, the result is 72,361. What is the largest of the three primes?
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. 