
theorem
  3943 is prime
proof
  now
    3943 = 2*1971 + 1; hence not 2 divides 3943 by NAT_4:9;
    3943 = 3*1314 + 1; hence not 3 divides 3943 by NAT_4:9;
    3943 = 5*788 + 3; hence not 5 divides 3943 by NAT_4:9;
    3943 = 7*563 + 2; hence not 7 divides 3943 by NAT_4:9;
    3943 = 11*358 + 5; hence not 11 divides 3943 by NAT_4:9;
    3943 = 13*303 + 4; hence not 13 divides 3943 by NAT_4:9;
    3943 = 17*231 + 16; hence not 17 divides 3943 by NAT_4:9;
    3943 = 19*207 + 10; hence not 19 divides 3943 by NAT_4:9;
    3943 = 23*171 + 10; hence not 23 divides 3943 by NAT_4:9;
    3943 = 29*135 + 28; hence not 29 divides 3943 by NAT_4:9;
    3943 = 31*127 + 6; hence not 31 divides 3943 by NAT_4:9;
    3943 = 37*106 + 21; hence not 37 divides 3943 by NAT_4:9;
    3943 = 41*96 + 7; hence not 41 divides 3943 by NAT_4:9;
    3943 = 43*91 + 30; hence not 43 divides 3943 by NAT_4:9;
    3943 = 47*83 + 42; hence not 47 divides 3943 by NAT_4:9;
    3943 = 53*74 + 21; hence not 53 divides 3943 by NAT_4:9;
    3943 = 59*66 + 49; hence not 59 divides 3943 by NAT_4:9;
    3943 = 61*64 + 39; hence not 61 divides 3943 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3943 & n is prime
  holds not n divides 3943 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
