
theorem
  4099 is prime
proof
  now
    4099 = 2*2049 + 1; hence not 2 divides 4099 by NAT_4:9;
    4099 = 3*1366 + 1; hence not 3 divides 4099 by NAT_4:9;
    4099 = 5*819 + 4; hence not 5 divides 4099 by NAT_4:9;
    4099 = 7*585 + 4; hence not 7 divides 4099 by NAT_4:9;
    4099 = 11*372 + 7; hence not 11 divides 4099 by NAT_4:9;
    4099 = 13*315 + 4; hence not 13 divides 4099 by NAT_4:9;
    4099 = 17*241 + 2; hence not 17 divides 4099 by NAT_4:9;
    4099 = 19*215 + 14; hence not 19 divides 4099 by NAT_4:9;
    4099 = 23*178 + 5; hence not 23 divides 4099 by NAT_4:9;
    4099 = 29*141 + 10; hence not 29 divides 4099 by NAT_4:9;
    4099 = 31*132 + 7; hence not 31 divides 4099 by NAT_4:9;
    4099 = 37*110 + 29; hence not 37 divides 4099 by NAT_4:9;
    4099 = 41*99 + 40; hence not 41 divides 4099 by NAT_4:9;
    4099 = 43*95 + 14; hence not 43 divides 4099 by NAT_4:9;
    4099 = 47*87 + 10; hence not 47 divides 4099 by NAT_4:9;
    4099 = 53*77 + 18; hence not 53 divides 4099 by NAT_4:9;
    4099 = 59*69 + 28; hence not 59 divides 4099 by NAT_4:9;
    4099 = 61*67 + 12; hence not 61 divides 4099 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4099 & n is prime
  holds not n divides 4099 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
