reserve d,i,j,k,m,n,p,q,x,k1,k2 for Nat,
  a,c,i1,i2,i3,i5 for Integer;

theorem
  256*256+1 is prime
proof
A2: 256*256 + 1 -'1 = 256*256 + 1 - 1 by XREAL_0:def 2
    .= 256*256 + 0;
  Fermat(4) divides ((3 |^ ((Fermat(4)-'1) div 2 )) - (-1)) by A2,Lm48,Th54;
  then (3 |^ ((Fermat(4)-'1) div 2)), (-1) are_congruent_mod Fermat(4);
  hence thesis by Th54,Th58;
end;
