Types of Prime Numbers

Time for a little math. I have been writing about lots of things and realized that math was deficient. How about a little fun with prime numbers?

Quick review: Prime numbers are natural numbers that have only two factors: 1 and the number.

Some special types of prime numbers (you didn't think that mathematicians would stop at one definition, did you?):

• Twin Primes - a set of two consecutive odd primes, which differ by 2. Examples: 3 and 5, 5 and 7, 11 and 13.
• Symmetric Primes, also called Euler Primes - a pair of prime numbers that are the same distance from a given number on the number line. Examples: Given 6, 5 and 7 are symmetric primes. Given 16, 3 and 29 are symmetric primes.
• Emirp - a prime number that remains prime when its digits are reversed. (Emirp, of course, if prime spelled backward!) Examples: 13 (31), 347 (743).
• Relatively Prime Numbers - numbers whose greatest common factor is prime. These numbers are not necessarily prime. This definition is referring to the relationship between numbers rather than the numbers themselves. Examples: 4 and 9, 10 and 27, 8 and 9.

So now, the questions to ponder/work on:

1. Can you find all of the symmetric primes for 24? (hint: there are more than 3 pairs - and no, I am not telling how many there are. That would spoil the fun!)
2. How many emirps exist between 1 and 200? (The number when it is listed its initial way - so 13 and 31 would each count as unique emirps.)

Ready..... Go!