
theorem
  3229 is prime
proof
  now
    3229 = 2*1614 + 1; hence not 2 divides 3229 by NAT_4:9;
    3229 = 3*1076 + 1; hence not 3 divides 3229 by NAT_4:9;
    3229 = 5*645 + 4; hence not 5 divides 3229 by NAT_4:9;
    3229 = 7*461 + 2; hence not 7 divides 3229 by NAT_4:9;
    3229 = 11*293 + 6; hence not 11 divides 3229 by NAT_4:9;
    3229 = 13*248 + 5; hence not 13 divides 3229 by NAT_4:9;
    3229 = 17*189 + 16; hence not 17 divides 3229 by NAT_4:9;
    3229 = 19*169 + 18; hence not 19 divides 3229 by NAT_4:9;
    3229 = 23*140 + 9; hence not 23 divides 3229 by NAT_4:9;
    3229 = 29*111 + 10; hence not 29 divides 3229 by NAT_4:9;
    3229 = 31*104 + 5; hence not 31 divides 3229 by NAT_4:9;
    3229 = 37*87 + 10; hence not 37 divides 3229 by NAT_4:9;
    3229 = 41*78 + 31; hence not 41 divides 3229 by NAT_4:9;
    3229 = 43*75 + 4; hence not 43 divides 3229 by NAT_4:9;
    3229 = 47*68 + 33; hence not 47 divides 3229 by NAT_4:9;
    3229 = 53*60 + 49; hence not 53 divides 3229 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3229 & n is prime
  holds not n divides 3229 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
