Eisenstein's Conjecture/Mistake

Source Work

1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.):

Eisenstein, Ferdinand Gotthold Max (1823-52)

Mistake

German mathematician who proposed the still unproved conjecture that numbers of the form $2^2 + 1, 2^{2^2} + 1, 2^{2^{2^2} } + 1, \ldots$ are prime.

Correction

This conjecture had been disproved in $1953$ by the discovery that $2^{2^{16} } + 1$ is composite, $45$ years before the publication of this dictionary.

This entry was updated by the $4$th edition, in which the above information was presented.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Eisenstein, Ferdinand Gotthold Max (1823-52)