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

theorem
  257 is prime
proof
  257 -'1 = 257 - 1 by XREAL_0:def 2
    .= 256 + 0;
  then Fermat(3) divides ((3 |^ ((Fermat(3)-'1) div 2 )) - (-1)) by Lm47,Th53;
  then (3 |^ ((Fermat(3)-'1) div 2)), (-1) are_congruent_mod Fermat(3);
  hence thesis by Th53,Th58;
end;
