A prime number is divisible only by 1 and itself. For example, 11 can only be evenly divided by 1 or 11. The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. The prime numbers seem to be randomly distributed, in that there is no discernible pattern to predict how often prime numbers occur. However, Stanford University mathematicians Robert Lemke Oliver and Kannan Soundararajan have found a strange pattern in the final digits of prime numbers.
Prime numbers greater than 5 end in 1, 3, 7, or 9. Even numbers greater than 2 can be divided by 2, and thus numbers ending in 0, 2, 4, 6, and 8 are not prime. Numbers ending in 5 can be divided by 5 and so are also not prime. If prime numbers were randomly distributed, there would be for a prime number like 242,413 a 25 percent chance that the next prime number would end in a 1, 25 percent for 3, 25 percent for 7, and 25 percent for 9. Each of the final four digits would be equally likely to occur. (The next prime is 242,419, by the way.)
This does not happen. Final digits tend to “repel” each other. In the first one billion primes, if a prime number ends in a 1, the next prime number ends in a 1 only 18 percent of the time. The same “repulsion” holds for the other three numbers. It also seems to hold for other numerical bases, which suggests that it’s not just that primes don’t like to appear with gaps of 10 between them. For example, it holds in base 3, which uses only the numbers 0, 1, and 2. As far as mathematicians have searched, the “repulsion” gets smaller but at a very slow rate.
Source: http://www.britannica.com/story/strange-pattern-found-in-prime-numbers
