
theorem
  937 is prime
proof
  now
    937 = 2*468 + 1; hence not 2 divides 937 by NAT_4:9;
    937 = 3*312 + 1; hence not 3 divides 937 by NAT_4:9;
    937 = 5*187 + 2; hence not 5 divides 937 by NAT_4:9;
    937 = 7*133 + 6; hence not 7 divides 937 by NAT_4:9;
    937 = 11*85 + 2; hence not 11 divides 937 by NAT_4:9;
    937 = 13*72 + 1; hence not 13 divides 937 by NAT_4:9;
    937 = 17*55 + 2; hence not 17 divides 937 by NAT_4:9;
    937 = 19*49 + 6; hence not 19 divides 937 by NAT_4:9;
    937 = 23*40 + 17; hence not 23 divides 937 by NAT_4:9;
    937 = 29*32 + 9; hence not 29 divides 937 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 937 & n is prime
  holds not n divides 937 by XPRIMET1:20;
  hence thesis by NAT_4:14;
end;
