Patterns in Prime Numbers
The different thing about primes is that there is no real pattern to their occurrence. They seem to appear randomly, however, we do know that all but two of them end in either 1, 3, 7, or 9. Other than that though, we have found no distinct pattern. This makes finding primes incredibly hard. If we knew they occurred every 24 number, they would be very easy to find. But, with their random appearances, each number has to be tested individually in order to determine if it is prime or not. Even with computers, this is a very grueling task. Recently, some progress has been made by graphing the prime numbers, but the patterns they form are very difficult to follow, and generating large primes with them would be difficult. Other, smaller patterns can be found in prime numbers, but eventually they terminate.
Some neat prime numbers that have patterns are 12345678901234567891. This is an ascending prime. Another neat pattern in primes is palindromic primes, and these read the same from front to back, such as 111191111, 919191919, and 123494321.