
theorem
  3163 is prime
proof
  now
    3163 = 2*1581 + 1; hence not 2 divides 3163 by NAT_4:9;
    3163 = 3*1054 + 1; hence not 3 divides 3163 by NAT_4:9;
    3163 = 5*632 + 3; hence not 5 divides 3163 by NAT_4:9;
    3163 = 7*451 + 6; hence not 7 divides 3163 by NAT_4:9;
    3163 = 11*287 + 6; hence not 11 divides 3163 by NAT_4:9;
    3163 = 13*243 + 4; hence not 13 divides 3163 by NAT_4:9;
    3163 = 17*186 + 1; hence not 17 divides 3163 by NAT_4:9;
    3163 = 19*166 + 9; hence not 19 divides 3163 by NAT_4:9;
    3163 = 23*137 + 12; hence not 23 divides 3163 by NAT_4:9;
    3163 = 29*109 + 2; hence not 29 divides 3163 by NAT_4:9;
    3163 = 31*102 + 1; hence not 31 divides 3163 by NAT_4:9;
    3163 = 37*85 + 18; hence not 37 divides 3163 by NAT_4:9;
    3163 = 41*77 + 6; hence not 41 divides 3163 by NAT_4:9;
    3163 = 43*73 + 24; hence not 43 divides 3163 by NAT_4:9;
    3163 = 47*67 + 14; hence not 47 divides 3163 by NAT_4:9;
    3163 = 53*59 + 36; hence not 53 divides 3163 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3163 & n is prime
  holds not n divides 3163 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
