Hunting Down the Curious Number 17
This week's Math Problem focused on an interesting pattern involving the prime number 17. In my attempts to learn more about this pattern, I came upon an Internet page of "Prime Curios" about the number 17. It was a fascinating read.
Some sample curios about the number 17:
 The only known prime that is equal to the sum of digits of its cube (173 = 4913, and 4 + 9 + 1 + 3 = 17)
 The only prime that is the average of two consecutive Fibonacci numbers.
 It takes 17 muscles to produce a smile.
 The least integer such that the sum of its digits in every base B = 2, 3, 4, 5, 6, 7, 8 is prime.
 17 * 65359477124183 = 1111111111111111
 There are exactly 17 ways to express 17 as the sum of one or more primes.
And so on...the above is but a glimpse.
And the number 17 is only one of a great number of numbers with "curios" on that site. So, I recommend you check out Prime Curios. Plan on spending a lot of time there...in fact, for every day for the rest of your life (or teaching career), you could check out curios about one or more numbers.
This web site is an appendage of the much larger web site The Prime Pages, organized by Chris Caldwell (University of Tennessee at Martin). It includes everything you would ever want to know about what is known about prime numbers.
