
theorem
  9439 is prime
proof
  now
    9439 = 2*4719 + 1; hence not 2 divides 9439 by NAT_4:9;
    9439 = 3*3146 + 1; hence not 3 divides 9439 by NAT_4:9;
    9439 = 5*1887 + 4; hence not 5 divides 9439 by NAT_4:9;
    9439 = 7*1348 + 3; hence not 7 divides 9439 by NAT_4:9;
    9439 = 11*858 + 1; hence not 11 divides 9439 by NAT_4:9;
    9439 = 13*726 + 1; hence not 13 divides 9439 by NAT_4:9;
    9439 = 17*555 + 4; hence not 17 divides 9439 by NAT_4:9;
    9439 = 19*496 + 15; hence not 19 divides 9439 by NAT_4:9;
    9439 = 23*410 + 9; hence not 23 divides 9439 by NAT_4:9;
    9439 = 29*325 + 14; hence not 29 divides 9439 by NAT_4:9;
    9439 = 31*304 + 15; hence not 31 divides 9439 by NAT_4:9;
    9439 = 37*255 + 4; hence not 37 divides 9439 by NAT_4:9;
    9439 = 41*230 + 9; hence not 41 divides 9439 by NAT_4:9;
    9439 = 43*219 + 22; hence not 43 divides 9439 by NAT_4:9;
    9439 = 47*200 + 39; hence not 47 divides 9439 by NAT_4:9;
    9439 = 53*178 + 5; hence not 53 divides 9439 by NAT_4:9;
    9439 = 59*159 + 58; hence not 59 divides 9439 by NAT_4:9;
    9439 = 61*154 + 45; hence not 61 divides 9439 by NAT_4:9;
    9439 = 67*140 + 59; hence not 67 divides 9439 by NAT_4:9;
    9439 = 71*132 + 67; hence not 71 divides 9439 by NAT_4:9;
    9439 = 73*129 + 22; hence not 73 divides 9439 by NAT_4:9;
    9439 = 79*119 + 38; hence not 79 divides 9439 by NAT_4:9;
    9439 = 83*113 + 60; hence not 83 divides 9439 by NAT_4:9;
    9439 = 89*106 + 5; hence not 89 divides 9439 by NAT_4:9;
    9439 = 97*97 + 30; hence not 97 divides 9439 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9439 & n is prime
  holds not n divides 9439 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
