Let's not forget about "fortunate" and "lucky" numbers!

According to wikipedia, fortunate numbers can be described as the following:

Given a positive integer n, we say that m>1 is a fortunate number if it is the smallest integer m such that p(n)+m is prime, where p(n) is the product of the first n primes.

For example, take n=1. Then p(1) = 2 since 2 is the smallest prime. We need the smallest m so that 2+m is prime. m=3 is our answer, so 3 is our first fortunate number!

As of today, all known fortunate numbers are also prime.

A "lucky" number can be found through a sort of sieve process. Take the list of all positive integers:

1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25…

First, we cross every second number off of our list:

1,3,5,7,9,11,13,15,17,19,21,23,25…

The second number left on our list is 3. This means that every 3rd number must be crossed off of our list:

1,3,7,9,13,15,19,21,25…

The third number left on our list is 7. This means that every 7th number can be crossed off of our list:

1,3,7,9,13,15,21,25,…

As you keep repeating this process, here is a list of the "lucky" numbers that you are left with:

1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79, 87, 93, 99, …

A lucky prime is a lucky number that is also a prime. It is unknown if there are infinitely many lucky primes.

For more information, check out these links!

http://en.wikipedia.org/wiki/Fortunate_number

http://en.wikipedia.org/wiki/Lucky_number