
theorem
  2381 is prime
proof
  now
    2381 = 2*1190 + 1; hence not 2 divides 2381 by NAT_4:9;
    2381 = 3*793 + 2; hence not 3 divides 2381 by NAT_4:9;
    2381 = 5*476 + 1; hence not 5 divides 2381 by NAT_4:9;
    2381 = 7*340 + 1; hence not 7 divides 2381 by NAT_4:9;
    2381 = 11*216 + 5; hence not 11 divides 2381 by NAT_4:9;
    2381 = 13*183 + 2; hence not 13 divides 2381 by NAT_4:9;
    2381 = 17*140 + 1; hence not 17 divides 2381 by NAT_4:9;
    2381 = 19*125 + 6; hence not 19 divides 2381 by NAT_4:9;
    2381 = 23*103 + 12; hence not 23 divides 2381 by NAT_4:9;
    2381 = 29*82 + 3; hence not 29 divides 2381 by NAT_4:9;
    2381 = 31*76 + 25; hence not 31 divides 2381 by NAT_4:9;
    2381 = 37*64 + 13; hence not 37 divides 2381 by NAT_4:9;
    2381 = 41*58 + 3; hence not 41 divides 2381 by NAT_4:9;
    2381 = 43*55 + 16; hence not 43 divides 2381 by NAT_4:9;
    2381 = 47*50 + 31; hence not 47 divides 2381 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2381 & n is prime
  holds not n divides 2381 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
