If you could pan back far enough, you’d see a kitten eating a cheeseburger

But you’d need a lot more prime numbers than we know about today.

I love stories like this:

Because prime numbers are indivisible (except by 1 and themselves), and because all other numbers can be written as multiples of them, they are often regarded as the “atoms” of the math world. Despite their importance, the distribution of prime numbers among the integers is still a mystery. There is no pattern dictating which numbers will be prime or how far apart successive primes will be.

The seeming randomness of the primes makes the pattern found in “Ulam spirals” very strange indeed.

In 1963, the mathematician Stanislaw Ulam…

…if I could find a picture of that guy in a swimsuit I’ll betcha he’d be my next big google bomb…

…noticed an odd pattern while doodling in his notebook during a presentation: When integers are written in a spiral, prime numbers always seem to fall along diagonal lines.

This in itself wasn’t so surprising, because all prime numbers except for the number 2 are odd, and diagonal lines in integer spirals are alternately odd and even. Much more startling was the tendency of prime numbers to lie on some diagonals more than others — and this happens regardless of whether you start with 1 in the middle, or any other number.

Even when you zoom out to a much larger scale, as in the plot of hundreds of numbers below, you can see clear diagonal lines of primes (black dots), with some lines stronger than others.

That looks like:

There are mathematical conjectures as to why this prime pattern emerges, but nothing has been proven.

Betcha the problem is we just haven’t discovered enough prime numbers yet. If we could zoom back on that picture far enough, with enough data points, it turns into:

The universe: it makes sense.

UPDATE - Dad29 is intrigued by the prospect of Stanislaw Ulam in a bikini. Back off, man. That’s my google bomb!