
theorem
  2647 is prime
proof
  now
    2647 = 2*1323 + 1; hence not 2 divides 2647 by NAT_4:9;
    2647 = 3*882 + 1; hence not 3 divides 2647 by NAT_4:9;
    2647 = 5*529 + 2; hence not 5 divides 2647 by NAT_4:9;
    2647 = 7*378 + 1; hence not 7 divides 2647 by NAT_4:9;
    2647 = 11*240 + 7; hence not 11 divides 2647 by NAT_4:9;
    2647 = 13*203 + 8; hence not 13 divides 2647 by NAT_4:9;
    2647 = 17*155 + 12; hence not 17 divides 2647 by NAT_4:9;
    2647 = 19*139 + 6; hence not 19 divides 2647 by NAT_4:9;
    2647 = 23*115 + 2; hence not 23 divides 2647 by NAT_4:9;
    2647 = 29*91 + 8; hence not 29 divides 2647 by NAT_4:9;
    2647 = 31*85 + 12; hence not 31 divides 2647 by NAT_4:9;
    2647 = 37*71 + 20; hence not 37 divides 2647 by NAT_4:9;
    2647 = 41*64 + 23; hence not 41 divides 2647 by NAT_4:9;
    2647 = 43*61 + 24; hence not 43 divides 2647 by NAT_4:9;
    2647 = 47*56 + 15; hence not 47 divides 2647 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2647 & n is prime
  holds not n divides 2647 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
