acc:=1700
(* Attention! this is an accuracy dependent formula,
if you give a lower accuracy then necessary ;
you'll get WRONG results *)
m:=228 (* m is an even integer *)
p:=m-1
q:=m+1
(* If (p,q) are twin primes then the
statement (ask) is true *)
f1:=q^p+p^q
f2:=2*(Cosh[q*ArcTanh[Sqrt[1-(2/p)^2]]]+
(Cosh[p*ArcTanh[Sqrt[1-(2/q)^2]]]))
ff2:=Rationalize[N[f2,acc]]
fonk1:=f1-ff2
(* the twin primes are given as (m+1)and(m-1)for (4-400)
m , taken from the following table *)
(* 4 6 12 18 30 42 60 72 102 108 138 150
180 192 198 228 240 270 282 312 348 *)
ask:=IntegerQ[fonk1/(p*q)]
ask
True