
theorem
  1237 is prime
proof
  now
    1237 = 2*618 + 1; hence not 2 divides 1237 by NAT_4:9;
    1237 = 3*412 + 1; hence not 3 divides 1237 by NAT_4:9;
    1237 = 5*247 + 2; hence not 5 divides 1237 by NAT_4:9;
    1237 = 7*176 + 5; hence not 7 divides 1237 by NAT_4:9;
    1237 = 11*112 + 5; hence not 11 divides 1237 by NAT_4:9;
    1237 = 13*95 + 2; hence not 13 divides 1237 by NAT_4:9;
    1237 = 17*72 + 13; hence not 17 divides 1237 by NAT_4:9;
    1237 = 19*65 + 2; hence not 19 divides 1237 by NAT_4:9;
    1237 = 23*53 + 18; hence not 23 divides 1237 by NAT_4:9;
    1237 = 29*42 + 19; hence not 29 divides 1237 by NAT_4:9;
    1237 = 31*39 + 28; hence not 31 divides 1237 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1237 & n is prime
  holds not n divides 1237 by XPRIMET1:22;
  hence thesis by NAT_4:14;
