An interesting discovery may be imminent regarding whether prime numbers appear randomly in the sequence of whole numbers. It has not yet been shown that the occurrence of prime numbers - 2, 3, 5, 7, 11, 13, etc - follows a pattern, or that there is definitely no pattern. Now Pradeep Kumar and colleagues at Boston University have found that the increments in the distances between consecutive primes are not random, but have some rudimentary predictability. For the first few primes the distances are 1, 2, 2, 4 and 2 and the increments are +1, 0, +2 and -2.
The researchers find for example that positive values are almost every time followed by corresponding negative values. These studies, the researchers say, may have consequences for understanding patterns in nature that depend on prime numbers.
Further reading
Nature Science Update www.nature.com/nsu/030317/030317-13.html.
P Kumar, P C Ivanov and H E Stanley Information entropy and correlations in prime numbers http://xxx.lanl.gov/abs/cond-mat/0303110 (2003).