119. Perfect Numbers

According to Euclid, one of the founding father of Modern Mathematics, a Perfect Number is one which is exactly equal to the sum of all its divisors. A divisor is any number, which divides the given number, without leaving any remainder.

The first Perfect Number is 6. Its divisors 1, 2, and 3 add up to 6, which is the number itself. The second Perfect Number is 28. Its divisors 1, 2, 4, 7 and 14 add up to 28, the number itself.

Greeks knew the third and the fourth Perfect Numbers as 496 and 8128. In the 15th century, the fifth Perfect Number was found to be 33,550,336–a number with eight digits in it.

Four more Perfect Numbers were discovered in the next 3 centuries. The ninth Perfect Number has 37 digits in it! In 1876, the tenth Perfect number was discovered and it has 77 digits in it.

The largest known Perfect Number, the 27th in the list, has an astounding 26,790 digits in it. The number would occupy 300 lines in a paper, when written down. It was discovered with the help of a computer in 1979.

Many puzzles linger on in the minds of the mathematicians. Why the Perfect Numbers are always even numbers? Can we have an odd Perfect Number? Is there a limiting value or can we always find a Perfect Number greater than all the known ones?

Hope the mathematical research will find the answers for all these questions in the future.

Visalakshi Ramani