
theorem
  3167 is prime
proof
  now
    3167 = 2*1583 + 1; hence not 2 divides 3167 by NAT_4:9;
    3167 = 3*1055 + 2; hence not 3 divides 3167 by NAT_4:9;
    3167 = 5*633 + 2; hence not 5 divides 3167 by NAT_4:9;
    3167 = 7*452 + 3; hence not 7 divides 3167 by NAT_4:9;
    3167 = 11*287 + 10; hence not 11 divides 3167 by NAT_4:9;
    3167 = 13*243 + 8; hence not 13 divides 3167 by NAT_4:9;
    3167 = 17*186 + 5; hence not 17 divides 3167 by NAT_4:9;
    3167 = 19*166 + 13; hence not 19 divides 3167 by NAT_4:9;
    3167 = 23*137 + 16; hence not 23 divides 3167 by NAT_4:9;
    3167 = 29*109 + 6; hence not 29 divides 3167 by NAT_4:9;
    3167 = 31*102 + 5; hence not 31 divides 3167 by NAT_4:9;
    3167 = 37*85 + 22; hence not 37 divides 3167 by NAT_4:9;
    3167 = 41*77 + 10; hence not 41 divides 3167 by NAT_4:9;
    3167 = 43*73 + 28; hence not 43 divides 3167 by NAT_4:9;
    3167 = 47*67 + 18; hence not 47 divides 3167 by NAT_4:9;
    3167 = 53*59 + 40; hence not 53 divides 3167 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3167 & n is prime
  holds not n divides 3167 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
