## Celebrate The Math Holiday Of ‘Perfect Number Day’ This June 28th

“Many candidate Mersenne primes have been shot down by showing they can be factored, usually into two primes. Just as 2047 = 23 * 89, many other candidate Mersenne primes have been shown not to be. In 1903, it was already known that (2

^{67}– 1) was not a Mersenne prime, but no one knew what its factors were. Frank Nelson Cole gave a talk to the American Mathematical Society entitled “On the Factorization of Large Numbers.” On the left side of the board, he computed (2^{67}– 1), which he showed equaled 147,573,952,589,676,412,927. On the right, he wrote 193,707,721 × 761,838,257,287, and spend his hour lecture saying nothing and working it out.At the end, when he showed both sides were equal, he sat down to a standing ovation, allegedly the first one ever given at a mathematics talk.”

We might feel that some numbers are better than others, but in mathematics, there really is a definition for a “perfect” number. If you take all the factors of a number except itself, add them up, and it equals the original number, your number is perfect. So 6 is a perfect number, because its factors, other than itself, are 3, 2, and 1, and 3+2+1=6. The next perfect number is 28: 14,7, 4, 2, and 1 are its other factors. These are the only two perfect numbers under 100, and it makes June 28th the perfect day to celebrate the perfect numbers.