
theorem
  9433 is prime
proof
  now
    9433 = 2*4716 + 1; hence not 2 divides 9433 by NAT_4:9;
    9433 = 3*3144 + 1; hence not 3 divides 9433 by NAT_4:9;
    9433 = 5*1886 + 3; hence not 5 divides 9433 by NAT_4:9;
    9433 = 7*1347 + 4; hence not 7 divides 9433 by NAT_4:9;
    9433 = 11*857 + 6; hence not 11 divides 9433 by NAT_4:9;
    9433 = 13*725 + 8; hence not 13 divides 9433 by NAT_4:9;
    9433 = 17*554 + 15; hence not 17 divides 9433 by NAT_4:9;
    9433 = 19*496 + 9; hence not 19 divides 9433 by NAT_4:9;
    9433 = 23*410 + 3; hence not 23 divides 9433 by NAT_4:9;
    9433 = 29*325 + 8; hence not 29 divides 9433 by NAT_4:9;
    9433 = 31*304 + 9; hence not 31 divides 9433 by NAT_4:9;
    9433 = 37*254 + 35; hence not 37 divides 9433 by NAT_4:9;
    9433 = 41*230 + 3; hence not 41 divides 9433 by NAT_4:9;
    9433 = 43*219 + 16; hence not 43 divides 9433 by NAT_4:9;
    9433 = 47*200 + 33; hence not 47 divides 9433 by NAT_4:9;
    9433 = 53*177 + 52; hence not 53 divides 9433 by NAT_4:9;
    9433 = 59*159 + 52; hence not 59 divides 9433 by NAT_4:9;
    9433 = 61*154 + 39; hence not 61 divides 9433 by NAT_4:9;
    9433 = 67*140 + 53; hence not 67 divides 9433 by NAT_4:9;
    9433 = 71*132 + 61; hence not 71 divides 9433 by NAT_4:9;
    9433 = 73*129 + 16; hence not 73 divides 9433 by NAT_4:9;
    9433 = 79*119 + 32; hence not 79 divides 9433 by NAT_4:9;
    9433 = 83*113 + 54; hence not 83 divides 9433 by NAT_4:9;
    9433 = 89*105 + 88; hence not 89 divides 9433 by NAT_4:9;
    9433 = 97*97 + 24; hence not 97 divides 9433 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9433 & n is prime
  holds not n divides 9433 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
