
theorem
  2389 is prime
proof
  now
    2389 = 2*1194 + 1; hence not 2 divides 2389 by NAT_4:9;
    2389 = 3*796 + 1; hence not 3 divides 2389 by NAT_4:9;
    2389 = 5*477 + 4; hence not 5 divides 2389 by NAT_4:9;
    2389 = 7*341 + 2; hence not 7 divides 2389 by NAT_4:9;
    2389 = 11*217 + 2; hence not 11 divides 2389 by NAT_4:9;
    2389 = 13*183 + 10; hence not 13 divides 2389 by NAT_4:9;
    2389 = 17*140 + 9; hence not 17 divides 2389 by NAT_4:9;
    2389 = 19*125 + 14; hence not 19 divides 2389 by NAT_4:9;
    2389 = 23*103 + 20; hence not 23 divides 2389 by NAT_4:9;
    2389 = 29*82 + 11; hence not 29 divides 2389 by NAT_4:9;
    2389 = 31*77 + 2; hence not 31 divides 2389 by NAT_4:9;
    2389 = 37*64 + 21; hence not 37 divides 2389 by NAT_4:9;
    2389 = 41*58 + 11; hence not 41 divides 2389 by NAT_4:9;
    2389 = 43*55 + 24; hence not 43 divides 2389 by NAT_4:9;
    2389 = 47*50 + 39; hence not 47 divides 2389 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2389 & n is prime
  holds not n divides 2389 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
