
theorem
  9403 is prime
proof
  now
    9403 = 2*4701 + 1; hence not 2 divides 9403 by NAT_4:9;
    9403 = 3*3134 + 1; hence not 3 divides 9403 by NAT_4:9;
    9403 = 5*1880 + 3; hence not 5 divides 9403 by NAT_4:9;
    9403 = 7*1343 + 2; hence not 7 divides 9403 by NAT_4:9;
    9403 = 11*854 + 9; hence not 11 divides 9403 by NAT_4:9;
    9403 = 13*723 + 4; hence not 13 divides 9403 by NAT_4:9;
    9403 = 17*553 + 2; hence not 17 divides 9403 by NAT_4:9;
    9403 = 19*494 + 17; hence not 19 divides 9403 by NAT_4:9;
    9403 = 23*408 + 19; hence not 23 divides 9403 by NAT_4:9;
    9403 = 29*324 + 7; hence not 29 divides 9403 by NAT_4:9;
    9403 = 31*303 + 10; hence not 31 divides 9403 by NAT_4:9;
    9403 = 37*254 + 5; hence not 37 divides 9403 by NAT_4:9;
    9403 = 41*229 + 14; hence not 41 divides 9403 by NAT_4:9;
    9403 = 43*218 + 29; hence not 43 divides 9403 by NAT_4:9;
    9403 = 47*200 + 3; hence not 47 divides 9403 by NAT_4:9;
    9403 = 53*177 + 22; hence not 53 divides 9403 by NAT_4:9;
    9403 = 59*159 + 22; hence not 59 divides 9403 by NAT_4:9;
    9403 = 61*154 + 9; hence not 61 divides 9403 by NAT_4:9;
    9403 = 67*140 + 23; hence not 67 divides 9403 by NAT_4:9;
    9403 = 71*132 + 31; hence not 71 divides 9403 by NAT_4:9;
    9403 = 73*128 + 59; hence not 73 divides 9403 by NAT_4:9;
    9403 = 79*119 + 2; hence not 79 divides 9403 by NAT_4:9;
    9403 = 83*113 + 24; hence not 83 divides 9403 by NAT_4:9;
    9403 = 89*105 + 58; hence not 89 divides 9403 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9403 & n is prime
  holds not n divides 9403 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
