
theorem
  3919 is prime
proof
  now
    3919 = 2*1959 + 1; hence not 2 divides 3919 by NAT_4:9;
    3919 = 3*1306 + 1; hence not 3 divides 3919 by NAT_4:9;
    3919 = 5*783 + 4; hence not 5 divides 3919 by NAT_4:9;
    3919 = 7*559 + 6; hence not 7 divides 3919 by NAT_4:9;
    3919 = 11*356 + 3; hence not 11 divides 3919 by NAT_4:9;
    3919 = 13*301 + 6; hence not 13 divides 3919 by NAT_4:9;
    3919 = 17*230 + 9; hence not 17 divides 3919 by NAT_4:9;
    3919 = 19*206 + 5; hence not 19 divides 3919 by NAT_4:9;
    3919 = 23*170 + 9; hence not 23 divides 3919 by NAT_4:9;
    3919 = 29*135 + 4; hence not 29 divides 3919 by NAT_4:9;
    3919 = 31*126 + 13; hence not 31 divides 3919 by NAT_4:9;
    3919 = 37*105 + 34; hence not 37 divides 3919 by NAT_4:9;
    3919 = 41*95 + 24; hence not 41 divides 3919 by NAT_4:9;
    3919 = 43*91 + 6; hence not 43 divides 3919 by NAT_4:9;
    3919 = 47*83 + 18; hence not 47 divides 3919 by NAT_4:9;
    3919 = 53*73 + 50; hence not 53 divides 3919 by NAT_4:9;
    3919 = 59*66 + 25; hence not 59 divides 3919 by NAT_4:9;
    3919 = 61*64 + 15; hence not 61 divides 3919 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3919 & n is prime
  holds not n divides 3919 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
