
theorem
  9293 is prime
proof
  now
    9293 = 2*4646 + 1; hence not 2 divides 9293 by NAT_4:9;
    9293 = 3*3097 + 2; hence not 3 divides 9293 by NAT_4:9;
    9293 = 5*1858 + 3; hence not 5 divides 9293 by NAT_4:9;
    9293 = 7*1327 + 4; hence not 7 divides 9293 by NAT_4:9;
    9293 = 11*844 + 9; hence not 11 divides 9293 by NAT_4:9;
    9293 = 13*714 + 11; hence not 13 divides 9293 by NAT_4:9;
    9293 = 17*546 + 11; hence not 17 divides 9293 by NAT_4:9;
    9293 = 19*489 + 2; hence not 19 divides 9293 by NAT_4:9;
    9293 = 23*404 + 1; hence not 23 divides 9293 by NAT_4:9;
    9293 = 29*320 + 13; hence not 29 divides 9293 by NAT_4:9;
    9293 = 31*299 + 24; hence not 31 divides 9293 by NAT_4:9;
    9293 = 37*251 + 6; hence not 37 divides 9293 by NAT_4:9;
    9293 = 41*226 + 27; hence not 41 divides 9293 by NAT_4:9;
    9293 = 43*216 + 5; hence not 43 divides 9293 by NAT_4:9;
    9293 = 47*197 + 34; hence not 47 divides 9293 by NAT_4:9;
    9293 = 53*175 + 18; hence not 53 divides 9293 by NAT_4:9;
    9293 = 59*157 + 30; hence not 59 divides 9293 by NAT_4:9;
    9293 = 61*152 + 21; hence not 61 divides 9293 by NAT_4:9;
    9293 = 67*138 + 47; hence not 67 divides 9293 by NAT_4:9;
    9293 = 71*130 + 63; hence not 71 divides 9293 by NAT_4:9;
    9293 = 73*127 + 22; hence not 73 divides 9293 by NAT_4:9;
    9293 = 79*117 + 50; hence not 79 divides 9293 by NAT_4:9;
    9293 = 83*111 + 80; hence not 83 divides 9293 by NAT_4:9;
    9293 = 89*104 + 37; hence not 89 divides 9293 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9293 & n is prime
  holds not n divides 9293 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
