Feit-Thompson Conjecture/Stronger/Mistake/Second Edition

Source Work

1997: David Wells: Curious and Interesting Numbers (2nd ed.):

The Dictionary

$17$

Mistake

The only known prime values for which $p^p - 1$ and $q^q - 1$ have a common factor less than $400,000$ are $17$ and $3313$. The common factor is $112,643$.

Correction

This is of course false, because $p^p - 1$ and $q^q - 1$ have the obvious common factor $2$.

It appears that the second edition compounded the mistake reported in the first edition

The only known prime values for which $p^q - 1$ and $q^p - 1$ have a common factor less than $400,000$ are $17$ and $3313$. The common factor is $112,643$.

by confusing the $p$s and $q$s.

The Stronger Feit-Thompson Conjecture actually states:

There exist no distinct prime numbers $p$ and $q$ such that:

$\dfrac {p^q - 1} {p - 1}$ and $\dfrac {q^p - 1} {q - 1}$ are not coprime.

Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $17$