
theorem
  2287 is prime
proof
  now
    2287 = 2*1143 + 1; hence not 2 divides 2287 by NAT_4:9;
    2287 = 3*762 + 1; hence not 3 divides 2287 by NAT_4:9;
    2287 = 5*457 + 2; hence not 5 divides 2287 by NAT_4:9;
    2287 = 7*326 + 5; hence not 7 divides 2287 by NAT_4:9;
    2287 = 11*207 + 10; hence not 11 divides 2287 by NAT_4:9;
    2287 = 13*175 + 12; hence not 13 divides 2287 by NAT_4:9;
    2287 = 17*134 + 9; hence not 17 divides 2287 by NAT_4:9;
    2287 = 19*120 + 7; hence not 19 divides 2287 by NAT_4:9;
    2287 = 23*99 + 10; hence not 23 divides 2287 by NAT_4:9;
    2287 = 29*78 + 25; hence not 29 divides 2287 by NAT_4:9;
    2287 = 31*73 + 24; hence not 31 divides 2287 by NAT_4:9;
    2287 = 37*61 + 30; hence not 37 divides 2287 by NAT_4:9;
    2287 = 41*55 + 32; hence not 41 divides 2287 by NAT_4:9;
    2287 = 43*53 + 8; hence not 43 divides 2287 by NAT_4:9;
    2287 = 47*48 + 31; hence not 47 divides 2287 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2287 & n is prime
  holds not n divides 2287 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
