Feit-Thompson Conjecture

Concerns Primes $p$ and $q$ for which $p^q-1$ and $q^p-1$ have a common factor. The only $(p, q)$ pair with both values less than 400,000 is (17, 3313), with a common factor 112,643.

References

Wells, D. G. The Penguin Dictionary of Curious and Interesting Numbers. London: Penguin, p. 17, 1986.