
theorem
  9419 is prime
proof
  now
    9419 = 2*4709 + 1; hence not 2 divides 9419 by NAT_4:9;
    9419 = 3*3139 + 2; hence not 3 divides 9419 by NAT_4:9;
    9419 = 5*1883 + 4; hence not 5 divides 9419 by NAT_4:9;
    9419 = 7*1345 + 4; hence not 7 divides 9419 by NAT_4:9;
    9419 = 11*856 + 3; hence not 11 divides 9419 by NAT_4:9;
    9419 = 13*724 + 7; hence not 13 divides 9419 by NAT_4:9;
    9419 = 17*554 + 1; hence not 17 divides 9419 by NAT_4:9;
    9419 = 19*495 + 14; hence not 19 divides 9419 by NAT_4:9;
    9419 = 23*409 + 12; hence not 23 divides 9419 by NAT_4:9;
    9419 = 29*324 + 23; hence not 29 divides 9419 by NAT_4:9;
    9419 = 31*303 + 26; hence not 31 divides 9419 by NAT_4:9;
    9419 = 37*254 + 21; hence not 37 divides 9419 by NAT_4:9;
    9419 = 41*229 + 30; hence not 41 divides 9419 by NAT_4:9;
    9419 = 43*219 + 2; hence not 43 divides 9419 by NAT_4:9;
    9419 = 47*200 + 19; hence not 47 divides 9419 by NAT_4:9;
    9419 = 53*177 + 38; hence not 53 divides 9419 by NAT_4:9;
    9419 = 59*159 + 38; hence not 59 divides 9419 by NAT_4:9;
    9419 = 61*154 + 25; hence not 61 divides 9419 by NAT_4:9;
    9419 = 67*140 + 39; hence not 67 divides 9419 by NAT_4:9;
    9419 = 71*132 + 47; hence not 71 divides 9419 by NAT_4:9;
    9419 = 73*129 + 2; hence not 73 divides 9419 by NAT_4:9;
    9419 = 79*119 + 18; hence not 79 divides 9419 by NAT_4:9;
    9419 = 83*113 + 40; hence not 83 divides 9419 by NAT_4:9;
    9419 = 89*105 + 74; hence not 89 divides 9419 by NAT_4:9;
    9419 = 97*97 + 10; hence not 97 divides 9419 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9419 & n is prime
  holds not n divides 9419 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
