
theorem
  2237 is prime
proof
  now
    2237 = 2*1118 + 1; hence not 2 divides 2237 by NAT_4:9;
    2237 = 3*745 + 2; hence not 3 divides 2237 by NAT_4:9;
    2237 = 5*447 + 2; hence not 5 divides 2237 by NAT_4:9;
    2237 = 7*319 + 4; hence not 7 divides 2237 by NAT_4:9;
    2237 = 11*203 + 4; hence not 11 divides 2237 by NAT_4:9;
    2237 = 13*172 + 1; hence not 13 divides 2237 by NAT_4:9;
    2237 = 17*131 + 10; hence not 17 divides 2237 by NAT_4:9;
    2237 = 19*117 + 14; hence not 19 divides 2237 by NAT_4:9;
    2237 = 23*97 + 6; hence not 23 divides 2237 by NAT_4:9;
    2237 = 29*77 + 4; hence not 29 divides 2237 by NAT_4:9;
    2237 = 31*72 + 5; hence not 31 divides 2237 by NAT_4:9;
    2237 = 37*60 + 17; hence not 37 divides 2237 by NAT_4:9;
    2237 = 41*54 + 23; hence not 41 divides 2237 by NAT_4:9;
    2237 = 43*52 + 1; hence not 43 divides 2237 by NAT_4:9;
    2237 = 47*47 + 28; hence not 47 divides 2237 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2237 & n is prime
  holds not n divides 2237 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
