
theorem
  2383 is prime
proof
  now
    2383 = 2*1191 + 1; hence not 2 divides 2383 by NAT_4:9;
    2383 = 3*794 + 1; hence not 3 divides 2383 by NAT_4:9;
    2383 = 5*476 + 3; hence not 5 divides 2383 by NAT_4:9;
    2383 = 7*340 + 3; hence not 7 divides 2383 by NAT_4:9;
    2383 = 11*216 + 7; hence not 11 divides 2383 by NAT_4:9;
    2383 = 13*183 + 4; hence not 13 divides 2383 by NAT_4:9;
    2383 = 17*140 + 3; hence not 17 divides 2383 by NAT_4:9;
    2383 = 19*125 + 8; hence not 19 divides 2383 by NAT_4:9;
    2383 = 23*103 + 14; hence not 23 divides 2383 by NAT_4:9;
    2383 = 29*82 + 5; hence not 29 divides 2383 by NAT_4:9;
    2383 = 31*76 + 27; hence not 31 divides 2383 by NAT_4:9;
    2383 = 37*64 + 15; hence not 37 divides 2383 by NAT_4:9;
    2383 = 41*58 + 5; hence not 41 divides 2383 by NAT_4:9;
    2383 = 43*55 + 18; hence not 43 divides 2383 by NAT_4:9;
    2383 = 47*50 + 33; hence not 47 divides 2383 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2383 & n is prime
  holds not n divides 2383 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
