
theorem
  1229 is prime
proof
  now
    1229 = 2*614 + 1; hence not 2 divides 1229 by NAT_4:9;
    1229 = 3*409 + 2; hence not 3 divides 1229 by NAT_4:9;
    1229 = 5*245 + 4; hence not 5 divides 1229 by NAT_4:9;
    1229 = 7*175 + 4; hence not 7 divides 1229 by NAT_4:9;
    1229 = 11*111 + 8; hence not 11 divides 1229 by NAT_4:9;
    1229 = 13*94 + 7; hence not 13 divides 1229 by NAT_4:9;
    1229 = 17*72 + 5; hence not 17 divides 1229 by NAT_4:9;
    1229 = 19*64 + 13; hence not 19 divides 1229 by NAT_4:9;
    1229 = 23*53 + 10; hence not 23 divides 1229 by NAT_4:9;
    1229 = 29*42 + 11; hence not 29 divides 1229 by NAT_4:9;
    1229 = 31*39 + 20; hence not 31 divides 1229 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1229 & n is prime
  holds not n divides 1229 by XPRIMET1:22;
  hence thesis by NAT_4:14;
end;
