There is only one set of five prime numbers that form an arithmetic sequence with a common difference of 6.  What is the sum of those five prime numbers?
To find a set of five prime numbers that form an arithmetic sequence with a common difference of 6, I need to start with the smallest possible prime number and keep adding 6 until I get five primes. The smallest possible prime number is 2, but if I add 6 to it, I get 8, which is not prime. The next smallest prime number is 3, but if I add 6 to it, I get 9, which is not prime. The next smallest prime number is 5, but if I add 6 to it, I get 11, which is prime. So far, I have two prime numbers in my sequence: 5 and 11. To get the third prime number, I need to add 6 to 11, which gives me 17, which is also prime. To get the fourth prime number, I need to add 6 to 17, which gives me 23, which is also prime. To get the fifth prime number, I need to add 6 to 23, which gives me 29, which is also prime. I have found my set of five prime numbers that form an arithmetic sequence with a common difference of 6: 5, 11, 17, 23, and 29. To find their sum, I just need to add them up: 5 + 11 + 17 + 23 + 29 = 85. 