
theorem
  2099 is prime
proof
  now
    2099 = 2*1049 + 1; hence not 2 divides 2099 by NAT_4:9;
    2099 = 3*699 + 2; hence not 3 divides 2099 by NAT_4:9;
    2099 = 5*419 + 4; hence not 5 divides 2099 by NAT_4:9;
    2099 = 7*299 + 6; hence not 7 divides 2099 by NAT_4:9;
    2099 = 11*190 + 9; hence not 11 divides 2099 by NAT_4:9;
    2099 = 13*161 + 6; hence not 13 divides 2099 by NAT_4:9;
    2099 = 17*123 + 8; hence not 17 divides 2099 by NAT_4:9;
    2099 = 19*110 + 9; hence not 19 divides 2099 by NAT_4:9;
    2099 = 23*91 + 6; hence not 23 divides 2099 by NAT_4:9;
    2099 = 29*72 + 11; hence not 29 divides 2099 by NAT_4:9;
    2099 = 31*67 + 22; hence not 31 divides 2099 by NAT_4:9;
    2099 = 37*56 + 27; hence not 37 divides 2099 by NAT_4:9;
    2099 = 41*51 + 8; hence not 41 divides 2099 by NAT_4:9;
    2099 = 43*48 + 35; hence not 43 divides 2099 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2099 & n is prime
  holds not n divides 2099 by XPRIMET1:28;
  hence thesis by NAT_4:14;
end;
