# Barlow's Prediction

Jump to navigation
Jump to search

## 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.

## Also see

## Source of Name

This entry was named for Peter Barlow.

## Sources

- 1962: Daniel Shanks:
*Solved and Unsolved Problems in Number Theory* - 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $28$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $28$