# Barlow's Prediction

## Prediction

Euler ascertained that $2^{31} - 1 = 2147483647$ is a prime number; and this is the greatest at present known to be such, and, consequently, the last of the above perfect numbers [that is, $2^{30}\left({2^{31} - 1}\right)$], which depends upon this, is the greatest perfect number known at present, and probably the greatest that ever will be discovered; for, as they are merely curious without being useful, it is not likely that any person will attempt to find one beyond it.

This statement was made by Peter Barlow, in his $1811$ work Elementary Investigation of the Theory of Numbers.

He repeated this statement word for word in his $1814$ work A New Mathematical and Philosophical Dictionary.

See the definition of Mersenne prime to follow up on exactly how inaccurate that prediction was.