
theorem
  3911 is prime
proof
  now
    3911 = 2*1955 + 1; hence not 2 divides 3911 by NAT_4:9;
    3911 = 3*1303 + 2; hence not 3 divides 3911 by NAT_4:9;
    3911 = 5*782 + 1; hence not 5 divides 3911 by NAT_4:9;
    3911 = 7*558 + 5; hence not 7 divides 3911 by NAT_4:9;
    3911 = 11*355 + 6; hence not 11 divides 3911 by NAT_4:9;
    3911 = 13*300 + 11; hence not 13 divides 3911 by NAT_4:9;
    3911 = 17*230 + 1; hence not 17 divides 3911 by NAT_4:9;
    3911 = 19*205 + 16; hence not 19 divides 3911 by NAT_4:9;
    3911 = 23*170 + 1; hence not 23 divides 3911 by NAT_4:9;
    3911 = 29*134 + 25; hence not 29 divides 3911 by NAT_4:9;
    3911 = 31*126 + 5; hence not 31 divides 3911 by NAT_4:9;
    3911 = 37*105 + 26; hence not 37 divides 3911 by NAT_4:9;
    3911 = 41*95 + 16; hence not 41 divides 3911 by NAT_4:9;
    3911 = 43*90 + 41; hence not 43 divides 3911 by NAT_4:9;
    3911 = 47*83 + 10; hence not 47 divides 3911 by NAT_4:9;
    3911 = 53*73 + 42; hence not 53 divides 3911 by NAT_4:9;
    3911 = 59*66 + 17; hence not 59 divides 3911 by NAT_4:9;
    3911 = 61*64 + 7; hence not 61 divides 3911 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3911 & n is prime
  holds not n divides 3911 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
