
theorem
  2089 is prime
proof
  now
    2089 = 2*1044 + 1; hence not 2 divides 2089 by NAT_4:9;
    2089 = 3*696 + 1; hence not 3 divides 2089 by NAT_4:9;
    2089 = 5*417 + 4; hence not 5 divides 2089 by NAT_4:9;
    2089 = 7*298 + 3; hence not 7 divides 2089 by NAT_4:9;
    2089 = 11*189 + 10; hence not 11 divides 2089 by NAT_4:9;
    2089 = 13*160 + 9; hence not 13 divides 2089 by NAT_4:9;
    2089 = 17*122 + 15; hence not 17 divides 2089 by NAT_4:9;
    2089 = 19*109 + 18; hence not 19 divides 2089 by NAT_4:9;
    2089 = 23*90 + 19; hence not 23 divides 2089 by NAT_4:9;
    2089 = 29*72 + 1; hence not 29 divides 2089 by NAT_4:9;
    2089 = 31*67 + 12; hence not 31 divides 2089 by NAT_4:9;
    2089 = 37*56 + 17; hence not 37 divides 2089 by NAT_4:9;
    2089 = 41*50 + 39; hence not 41 divides 2089 by NAT_4:9;
    2089 = 43*48 + 25; hence not 43 divides 2089 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2089 & n is prime
  holds not n divides 2089 by XPRIMET1:28;
  hence thesis by NAT_4:14;
end;
