
theorem
  2297 is prime
proof
  now
    2297 = 2*1148 + 1; hence not 2 divides 2297 by NAT_4:9;
    2297 = 3*765 + 2; hence not 3 divides 2297 by NAT_4:9;
    2297 = 5*459 + 2; hence not 5 divides 2297 by NAT_4:9;
    2297 = 7*328 + 1; hence not 7 divides 2297 by NAT_4:9;
    2297 = 11*208 + 9; hence not 11 divides 2297 by NAT_4:9;
    2297 = 13*176 + 9; hence not 13 divides 2297 by NAT_4:9;
    2297 = 17*135 + 2; hence not 17 divides 2297 by NAT_4:9;
    2297 = 19*120 + 17; hence not 19 divides 2297 by NAT_4:9;
    2297 = 23*99 + 20; hence not 23 divides 2297 by NAT_4:9;
    2297 = 29*79 + 6; hence not 29 divides 2297 by NAT_4:9;
    2297 = 31*74 + 3; hence not 31 divides 2297 by NAT_4:9;
    2297 = 37*62 + 3; hence not 37 divides 2297 by NAT_4:9;
    2297 = 41*56 + 1; hence not 41 divides 2297 by NAT_4:9;
    2297 = 43*53 + 18; hence not 43 divides 2297 by NAT_4:9;
    2297 = 47*48 + 41; hence not 47 divides 2297 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2297 & n is prime
  holds not n divides 2297 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
