
theorem
  2749 is prime
proof
  now
    2749 = 2*1374 + 1; hence not 2 divides 2749 by NAT_4:9;
    2749 = 3*916 + 1; hence not 3 divides 2749 by NAT_4:9;
    2749 = 5*549 + 4; hence not 5 divides 2749 by NAT_4:9;
    2749 = 7*392 + 5; hence not 7 divides 2749 by NAT_4:9;
    2749 = 11*249 + 10; hence not 11 divides 2749 by NAT_4:9;
    2749 = 13*211 + 6; hence not 13 divides 2749 by NAT_4:9;
    2749 = 17*161 + 12; hence not 17 divides 2749 by NAT_4:9;
    2749 = 19*144 + 13; hence not 19 divides 2749 by NAT_4:9;
    2749 = 23*119 + 12; hence not 23 divides 2749 by NAT_4:9;
    2749 = 29*94 + 23; hence not 29 divides 2749 by NAT_4:9;
    2749 = 31*88 + 21; hence not 31 divides 2749 by NAT_4:9;
    2749 = 37*74 + 11; hence not 37 divides 2749 by NAT_4:9;
    2749 = 41*67 + 2; hence not 41 divides 2749 by NAT_4:9;
    2749 = 43*63 + 40; hence not 43 divides 2749 by NAT_4:9;
    2749 = 47*58 + 23; hence not 47 divides 2749 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2749 & n is prime
  holds not n divides 2749 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
