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I have always loved exploring the powers of two. It is so natural for children to double numbers. When children count staring with 2, 4, ____  invariably they always say 6. They are pre-programed to count by twos.

I played  a game a few years ago with the children that was a challenging exercise in multiples of 3 and 7.

Last week we explored again the Sieve of Eratosthenes using a grid of 6 columns instead of the traditional ten. The children made an amazing discovery: every prime number except for 2 and 3 is one more than a multiple of 6 or one less than a multiple of 6.

The children are excited about the prospect of the multiple $1,000,000 prizes offered to the mathematician who can find a pattern in prime numbers that would predict the next prime. Hopefully, this will be a lifelong pursuit.

The Atoms of Mathematics