Feit-Thompson Conjecture

Author

Eric W. Weisstein
April 26, 2006

This notebook downloaded from http://mathworld.wolfram.com/notebooks/GroupTheory/Feit-ThompsonConjecture.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Feit-ThompsonConjecture.html.

©2006 Wolfram Research, Inc. except for portions noted otherwise

Code

FeitThompsonQ[p_Integer?PrimeQ,q_Integer?PrimeQ]:=
GCD[(p^q-1)/(p-1),(q^p-1)/(q-1)]!=1

FeitThompsonGCD[p_,q_]:=GCD[(p^q-1)/(p-1),(q^p-1)/(q-1)]

Check

FeitThompsonQ[17,3313]

FeitThompson[17,3313]

Search

PrimePi/@{400000,500000}

Prime/@%

a=33860; (*PrimePi[400000]*)
b=41538; (*PrimePi[500000]*)

Do[
If[
FeitThompsonQ[Prime[p],Prime[q]],
Print[{{p,Prime[p]},{q,Prime[q]}}]
],{p,a,b},{q,2,b}]