Primes classification

[Artur]

%S A127042 2, 3, 5, 7, 17, 19, 29, 31, 37, 41, 97, 127, 131, 211, 223,  
227, 229
%N A127042 Primes p such that denumerator of Sum_{k=1..p-1} 1/k^2} is  
square
%t A127042 a = {}; Do[If[Sqrt[Denominator[Sum[1/x^2, {x, 1, Prime[x] -  
1}]]] == Floor[Sqrt[Denominator[Sum[1/x^2, {x, 1, Prime[x] - 1}]]]],  
AppendTo[a, Prime[x]]], {x, 1, 50}]; a
%Y A127042 A061002, A034602, A127029
%O A127042 1
%K A127042 ,nonn,
%A A127042 Artur Jasinski (grafix at csl.pl), Jan 03 2007

Wolstenholme in 1862 proof that nominators always are square for each  
prime >=5
that mean for A127042={5, 7, 17, 19, 29, 31, 37, 41, 97, 127, 131, 211,  
223, 227, 229,...}
Sum_{k=1..p-1} 1/k^2} have form a^2/b^2

ARTUR