
theorem
  9413 is prime
proof
  now
    9413 = 2*4706 + 1; hence not 2 divides 9413 by NAT_4:9;
    9413 = 3*3137 + 2; hence not 3 divides 9413 by NAT_4:9;
    9413 = 5*1882 + 3; hence not 5 divides 9413 by NAT_4:9;
    9413 = 7*1344 + 5; hence not 7 divides 9413 by NAT_4:9;
    9413 = 11*855 + 8; hence not 11 divides 9413 by NAT_4:9;
    9413 = 13*724 + 1; hence not 13 divides 9413 by NAT_4:9;
    9413 = 17*553 + 12; hence not 17 divides 9413 by NAT_4:9;
    9413 = 19*495 + 8; hence not 19 divides 9413 by NAT_4:9;
    9413 = 23*409 + 6; hence not 23 divides 9413 by NAT_4:9;
    9413 = 29*324 + 17; hence not 29 divides 9413 by NAT_4:9;
    9413 = 31*303 + 20; hence not 31 divides 9413 by NAT_4:9;
    9413 = 37*254 + 15; hence not 37 divides 9413 by NAT_4:9;
    9413 = 41*229 + 24; hence not 41 divides 9413 by NAT_4:9;
    9413 = 43*218 + 39; hence not 43 divides 9413 by NAT_4:9;
    9413 = 47*200 + 13; hence not 47 divides 9413 by NAT_4:9;
    9413 = 53*177 + 32; hence not 53 divides 9413 by NAT_4:9;
    9413 = 59*159 + 32; hence not 59 divides 9413 by NAT_4:9;
    9413 = 61*154 + 19; hence not 61 divides 9413 by NAT_4:9;
    9413 = 67*140 + 33; hence not 67 divides 9413 by NAT_4:9;
    9413 = 71*132 + 41; hence not 71 divides 9413 by NAT_4:9;
    9413 = 73*128 + 69; hence not 73 divides 9413 by NAT_4:9;
    9413 = 79*119 + 12; hence not 79 divides 9413 by NAT_4:9;
    9413 = 83*113 + 34; hence not 83 divides 9413 by NAT_4:9;
    9413 = 89*105 + 68; hence not 89 divides 9413 by NAT_4:9;
    9413 = 97*97 + 4; hence not 97 divides 9413 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9413 & n is prime
  holds not n divides 9413 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
