Sometimes somebody finds a rule-of-thumb about some numbers that is somehow something special. An example of this is the Titus-Bode Law. This rough rule predicts the spacing of the planets in the Solar System. The relationship was first pointed out by Johann Titius in 1766 and was formulated as a mathematical expression by J.E. Bode in 1778. It led Bode to predict the existence of another planet (Ceres) between Mars and Jupiter in what we now recognize as the asteroid belt. It works for the moons, too; cool, huh? Except that we know of no reason WHY the T-B Law should work, though people have been looking for an explanation for years. Everybody’s gut feeling is that the T-B Law is trying to tell us SOMETHING about how gravity forms solar systems, but WHAT? It’s like discovering just the last page of one of Einstein’s manuscripts with some incredible formula like E=mc^2 on it and missing all the earlier pages that tells how he got there – a delicious mathematical mystery.

Here comes another one. Pradeep Kumar and other physicists at Boston University may have stumbled upon a surprising discovery about one of the deepest and best-studied questions in pure mathematics: whether or not prime numbers (numbers that cannot be divided without a remainder by any smaller number other than 1) appear randomly in the sequence of whole numbers.
The first few primes are 2, 3, 5, 7, 11 and 13. Kumar’s team looked at the increments in the intervals between consecutive primes. For example, the intervals between the first few are 1, 2, 2, 4 and 2. The increments are the differences between these successive intervals: +1, 0, +2 and -2. “Positive values are almost every time followed by corresponding negative values,” explains team member Plamen Ivanov. Their efforts also confirmed earlier work that a plot of the number of increments of different sizes shows oscillations with a period of three.

Big deal? Could be. Our most advanced encryption codes are based on prime numbers and the difficulty of factoring the product of two big ones. If somebody knew some shortcuts on how to look for big prime numbers, there’s no telling what they could do…