The Feit-Thompson conjecture asserts that there are no primes 
and 
for which 
and 
have a common factor.
Parker noticed that if this were true, it would greatly simplify the lengthy proof of the Feit-Thompson theorem that every
group of odd order is solvable. (Guy 1994, p. 81). However, the counterexample
(
,
)
with a common factor 
was subsequently found by Stephens (1971), demonstrating
that the conjecture is, in fact, false.
No other such pairs exist with both values less than 
.
and 
."
Math. Comput. 29, 1-6, 1975.Feit, W. and Thompson, J. G.
"A Solvability Criterion for Finite Groups and Some Consequences." Proc.
Nat. Acad. Sci. USA 48, 968-970, 1962.Feit, W. and Thompson,
J. G. "Solvability of Groups of Odd Order." Pacific J. Math. 13,
775-1029, 1963.Guy, R. K.