Barlow's Prediction
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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): $28$