
theorem
  6673 is prime
proof
  now
    6673 = 2*3336 + 1; hence not 2 divides 6673 by NAT_4:9;
    6673 = 3*2224 + 1; hence not 3 divides 6673 by NAT_4:9;
    6673 = 5*1334 + 3; hence not 5 divides 6673 by NAT_4:9;
    6673 = 7*953 + 2; hence not 7 divides 6673 by NAT_4:9;
    6673 = 11*606 + 7; hence not 11 divides 6673 by NAT_4:9;
    6673 = 13*513 + 4; hence not 13 divides 6673 by NAT_4:9;
    6673 = 17*392 + 9; hence not 17 divides 6673 by NAT_4:9;
    6673 = 19*351 + 4; hence not 19 divides 6673 by NAT_4:9;
    6673 = 23*290 + 3; hence not 23 divides 6673 by NAT_4:9;
    6673 = 29*230 + 3; hence not 29 divides 6673 by NAT_4:9;
    6673 = 31*215 + 8; hence not 31 divides 6673 by NAT_4:9;
    6673 = 37*180 + 13; hence not 37 divides 6673 by NAT_4:9;
    6673 = 41*162 + 31; hence not 41 divides 6673 by NAT_4:9;
    6673 = 43*155 + 8; hence not 43 divides 6673 by NAT_4:9;
    6673 = 47*141 + 46; hence not 47 divides 6673 by NAT_4:9;
    6673 = 53*125 + 48; hence not 53 divides 6673 by NAT_4:9;
    6673 = 59*113 + 6; hence not 59 divides 6673 by NAT_4:9;
    6673 = 61*109 + 24; hence not 61 divides 6673 by NAT_4:9;
    6673 = 67*99 + 40; hence not 67 divides 6673 by NAT_4:9;
    6673 = 71*93 + 70; hence not 71 divides 6673 by NAT_4:9;
    6673 = 73*91 + 30; hence not 73 divides 6673 by NAT_4:9;
    6673 = 79*84 + 37; hence not 79 divides 6673 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6673 & n is prime
  holds not n divides 6673 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
