
theorem
  2999 is prime
proof
  now
    2999 = 2*1499 + 1; hence not 2 divides 2999 by NAT_4:9;
    2999 = 3*999 + 2; hence not 3 divides 2999 by NAT_4:9;
    2999 = 5*599 + 4; hence not 5 divides 2999 by NAT_4:9;
    2999 = 7*428 + 3; hence not 7 divides 2999 by NAT_4:9;
    2999 = 11*272 + 7; hence not 11 divides 2999 by NAT_4:9;
    2999 = 13*230 + 9; hence not 13 divides 2999 by NAT_4:9;
    2999 = 17*176 + 7; hence not 17 divides 2999 by NAT_4:9;
    2999 = 19*157 + 16; hence not 19 divides 2999 by NAT_4:9;
    2999 = 23*130 + 9; hence not 23 divides 2999 by NAT_4:9;
    2999 = 29*103 + 12; hence not 29 divides 2999 by NAT_4:9;
    2999 = 31*96 + 23; hence not 31 divides 2999 by NAT_4:9;
    2999 = 37*81 + 2; hence not 37 divides 2999 by NAT_4:9;
    2999 = 41*73 + 6; hence not 41 divides 2999 by NAT_4:9;
    2999 = 43*69 + 32; hence not 43 divides 2999 by NAT_4:9;
    2999 = 47*63 + 38; hence not 47 divides 2999 by NAT_4:9;
    2999 = 53*56 + 31; hence not 53 divides 2999 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2999 & n is prime
  holds not n divides 2999 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
