
theorem
  2789 is prime
proof
  now
    2789 = 2*1394 + 1; hence not 2 divides 2789 by NAT_4:9;
    2789 = 3*929 + 2; hence not 3 divides 2789 by NAT_4:9;
    2789 = 5*557 + 4; hence not 5 divides 2789 by NAT_4:9;
    2789 = 7*398 + 3; hence not 7 divides 2789 by NAT_4:9;
    2789 = 11*253 + 6; hence not 11 divides 2789 by NAT_4:9;
    2789 = 13*214 + 7; hence not 13 divides 2789 by NAT_4:9;
    2789 = 17*164 + 1; hence not 17 divides 2789 by NAT_4:9;
    2789 = 19*146 + 15; hence not 19 divides 2789 by NAT_4:9;
    2789 = 23*121 + 6; hence not 23 divides 2789 by NAT_4:9;
    2789 = 29*96 + 5; hence not 29 divides 2789 by NAT_4:9;
    2789 = 31*89 + 30; hence not 31 divides 2789 by NAT_4:9;
    2789 = 37*75 + 14; hence not 37 divides 2789 by NAT_4:9;
    2789 = 41*68 + 1; hence not 41 divides 2789 by NAT_4:9;
    2789 = 43*64 + 37; hence not 43 divides 2789 by NAT_4:9;
    2789 = 47*59 + 16; hence not 47 divides 2789 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2789 & n is prime
  holds not n divides 2789 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
