
theorem
  3967 is prime
proof
  now
    3967 = 2*1983 + 1; hence not 2 divides 3967 by NAT_4:9;
    3967 = 3*1322 + 1; hence not 3 divides 3967 by NAT_4:9;
    3967 = 5*793 + 2; hence not 5 divides 3967 by NAT_4:9;
    3967 = 7*566 + 5; hence not 7 divides 3967 by NAT_4:9;
    3967 = 11*360 + 7; hence not 11 divides 3967 by NAT_4:9;
    3967 = 13*305 + 2; hence not 13 divides 3967 by NAT_4:9;
    3967 = 17*233 + 6; hence not 17 divides 3967 by NAT_4:9;
    3967 = 19*208 + 15; hence not 19 divides 3967 by NAT_4:9;
    3967 = 23*172 + 11; hence not 23 divides 3967 by NAT_4:9;
    3967 = 29*136 + 23; hence not 29 divides 3967 by NAT_4:9;
    3967 = 31*127 + 30; hence not 31 divides 3967 by NAT_4:9;
    3967 = 37*107 + 8; hence not 37 divides 3967 by NAT_4:9;
    3967 = 41*96 + 31; hence not 41 divides 3967 by NAT_4:9;
    3967 = 43*92 + 11; hence not 43 divides 3967 by NAT_4:9;
    3967 = 47*84 + 19; hence not 47 divides 3967 by NAT_4:9;
    3967 = 53*74 + 45; hence not 53 divides 3967 by NAT_4:9;
    3967 = 59*67 + 14; hence not 59 divides 3967 by NAT_4:9;
    3967 = 61*65 + 2; hence not 61 divides 3967 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3967 & n is prime
  holds not n divides 3967 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
