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

theorem
  17 is prime
proof
A2: 17 -'1 = 17 - 1 by XREAL_0:def 2
    .= 16 + 0;
  (Fermat(2) -'1) div 2 = 16*0 + 8 by A2,Th52;
  then Fermat(2) divides (3 |^ ((Fermat(2)-'1) div 2)) + 1 by Lm24;
  then Fermat(2) divides ((3 |^ ((Fermat(2)-'1) div 2 )) - (-1));
  then (3 |^ ((Fermat(2)-'1) div 2)), (-1) are_congruent_mod Fermat(2);
  hence thesis by Th52,Th58;
end;
