2,147,483,647/Historical Note

Historical Note on $2 \, 147 \, 483 \, 647$

$2 \, 147 \, 483 \, 647$ was one of the Mersenne numbers that Marin Mersenne predicted to be prime in his Cogitata Physico-Mathematica of $1644$.

It was Leonhard Paul Euler who demonstrated it to be prime, which he did in $1772$.

Barlow's 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.

Sources

• 1919: Leonard Eugene Dickson: History of the Theory of Numbers: Volume $\text { I }$ ... (previous) ... (next): Preface
• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $2^{229} - 1$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $2^{229} - 1$