
theorem
  3947 is prime
proof
  now
    3947 = 2*1973 + 1; hence not 2 divides 3947 by NAT_4:9;
    3947 = 3*1315 + 2; hence not 3 divides 3947 by NAT_4:9;
    3947 = 5*789 + 2; hence not 5 divides 3947 by NAT_4:9;
    3947 = 7*563 + 6; hence not 7 divides 3947 by NAT_4:9;
    3947 = 11*358 + 9; hence not 11 divides 3947 by NAT_4:9;
    3947 = 13*303 + 8; hence not 13 divides 3947 by NAT_4:9;
    3947 = 17*232 + 3; hence not 17 divides 3947 by NAT_4:9;
    3947 = 19*207 + 14; hence not 19 divides 3947 by NAT_4:9;
    3947 = 23*171 + 14; hence not 23 divides 3947 by NAT_4:9;
    3947 = 29*136 + 3; hence not 29 divides 3947 by NAT_4:9;
    3947 = 31*127 + 10; hence not 31 divides 3947 by NAT_4:9;
    3947 = 37*106 + 25; hence not 37 divides 3947 by NAT_4:9;
    3947 = 41*96 + 11; hence not 41 divides 3947 by NAT_4:9;
    3947 = 43*91 + 34; hence not 43 divides 3947 by NAT_4:9;
    3947 = 47*83 + 46; hence not 47 divides 3947 by NAT_4:9;
    3947 = 53*74 + 25; hence not 53 divides 3947 by NAT_4:9;
    3947 = 59*66 + 53; hence not 59 divides 3947 by NAT_4:9;
    3947 = 61*64 + 43; hence not 61 divides 3947 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3947 & n is prime
  holds not n divides 3947 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
