
theorem
  9283 is prime
proof
  now
    9283 = 2*4641 + 1; hence not 2 divides 9283 by NAT_4:9;
    9283 = 3*3094 + 1; hence not 3 divides 9283 by NAT_4:9;
    9283 = 5*1856 + 3; hence not 5 divides 9283 by NAT_4:9;
    9283 = 7*1326 + 1; hence not 7 divides 9283 by NAT_4:9;
    9283 = 11*843 + 10; hence not 11 divides 9283 by NAT_4:9;
    9283 = 13*714 + 1; hence not 13 divides 9283 by NAT_4:9;
    9283 = 17*546 + 1; hence not 17 divides 9283 by NAT_4:9;
    9283 = 19*488 + 11; hence not 19 divides 9283 by NAT_4:9;
    9283 = 23*403 + 14; hence not 23 divides 9283 by NAT_4:9;
    9283 = 29*320 + 3; hence not 29 divides 9283 by NAT_4:9;
    9283 = 31*299 + 14; hence not 31 divides 9283 by NAT_4:9;
    9283 = 37*250 + 33; hence not 37 divides 9283 by NAT_4:9;
    9283 = 41*226 + 17; hence not 41 divides 9283 by NAT_4:9;
    9283 = 43*215 + 38; hence not 43 divides 9283 by NAT_4:9;
    9283 = 47*197 + 24; hence not 47 divides 9283 by NAT_4:9;
    9283 = 53*175 + 8; hence not 53 divides 9283 by NAT_4:9;
    9283 = 59*157 + 20; hence not 59 divides 9283 by NAT_4:9;
    9283 = 61*152 + 11; hence not 61 divides 9283 by NAT_4:9;
    9283 = 67*138 + 37; hence not 67 divides 9283 by NAT_4:9;
    9283 = 71*130 + 53; hence not 71 divides 9283 by NAT_4:9;
    9283 = 73*127 + 12; hence not 73 divides 9283 by NAT_4:9;
    9283 = 79*117 + 40; hence not 79 divides 9283 by NAT_4:9;
    9283 = 83*111 + 70; hence not 83 divides 9283 by NAT_4:9;
    9283 = 89*104 + 27; hence not 89 divides 9283 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9283 & n is prime
  holds not n divides 9283 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
