
theorem
  2293 is prime
proof
  now
    2293 = 2*1146 + 1; hence not 2 divides 2293 by NAT_4:9;
    2293 = 3*764 + 1; hence not 3 divides 2293 by NAT_4:9;
    2293 = 5*458 + 3; hence not 5 divides 2293 by NAT_4:9;
    2293 = 7*327 + 4; hence not 7 divides 2293 by NAT_4:9;
    2293 = 11*208 + 5; hence not 11 divides 2293 by NAT_4:9;
    2293 = 13*176 + 5; hence not 13 divides 2293 by NAT_4:9;
    2293 = 17*134 + 15; hence not 17 divides 2293 by NAT_4:9;
    2293 = 19*120 + 13; hence not 19 divides 2293 by NAT_4:9;
    2293 = 23*99 + 16; hence not 23 divides 2293 by NAT_4:9;
    2293 = 29*79 + 2; hence not 29 divides 2293 by NAT_4:9;
    2293 = 31*73 + 30; hence not 31 divides 2293 by NAT_4:9;
    2293 = 37*61 + 36; hence not 37 divides 2293 by NAT_4:9;
    2293 = 41*55 + 38; hence not 41 divides 2293 by NAT_4:9;
    2293 = 43*53 + 14; hence not 43 divides 2293 by NAT_4:9;
    2293 = 47*48 + 37; hence not 47 divides 2293 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2293 & n is prime
  holds not n divides 2293 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
