
theorem
  2029 is prime
proof
  now
    2029 = 2*1014 + 1; hence not 2 divides 2029 by NAT_4:9;
    2029 = 3*676 + 1; hence not 3 divides 2029 by NAT_4:9;
    2029 = 5*405 + 4; hence not 5 divides 2029 by NAT_4:9;
    2029 = 7*289 + 6; hence not 7 divides 2029 by NAT_4:9;
    2029 = 11*184 + 5; hence not 11 divides 2029 by NAT_4:9;
    2029 = 13*156 + 1; hence not 13 divides 2029 by NAT_4:9;
    2029 = 17*119 + 6; hence not 17 divides 2029 by NAT_4:9;
    2029 = 19*106 + 15; hence not 19 divides 2029 by NAT_4:9;
    2029 = 23*88 + 5; hence not 23 divides 2029 by NAT_4:9;
    2029 = 29*69 + 28; hence not 29 divides 2029 by NAT_4:9;
    2029 = 31*65 + 14; hence not 31 divides 2029 by NAT_4:9;
    2029 = 37*54 + 31; hence not 37 divides 2029 by NAT_4:9;
    2029 = 41*49 + 20; hence not 41 divides 2029 by NAT_4:9;
    2029 = 43*47 + 8; hence not 43 divides 2029 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2029 & n is prime
  holds not n divides 2029 by XPRIMET1:28;
  hence thesis by NAT_4:14;
end;
