
theorem
  7333 is prime
proof
  now
    7333 = 2*3666 + 1; hence not 2 divides 7333 by NAT_4:9;
    7333 = 3*2444 + 1; hence not 3 divides 7333 by NAT_4:9;
    7333 = 5*1466 + 3; hence not 5 divides 7333 by NAT_4:9;
    7333 = 7*1047 + 4; hence not 7 divides 7333 by NAT_4:9;
    7333 = 11*666 + 7; hence not 11 divides 7333 by NAT_4:9;
    7333 = 13*564 + 1; hence not 13 divides 7333 by NAT_4:9;
    7333 = 17*431 + 6; hence not 17 divides 7333 by NAT_4:9;
    7333 = 19*385 + 18; hence not 19 divides 7333 by NAT_4:9;
    7333 = 23*318 + 19; hence not 23 divides 7333 by NAT_4:9;
    7333 = 29*252 + 25; hence not 29 divides 7333 by NAT_4:9;
    7333 = 31*236 + 17; hence not 31 divides 7333 by NAT_4:9;
    7333 = 37*198 + 7; hence not 37 divides 7333 by NAT_4:9;
    7333 = 41*178 + 35; hence not 41 divides 7333 by NAT_4:9;
    7333 = 43*170 + 23; hence not 43 divides 7333 by NAT_4:9;
    7333 = 47*156 + 1; hence not 47 divides 7333 by NAT_4:9;
    7333 = 53*138 + 19; hence not 53 divides 7333 by NAT_4:9;
    7333 = 59*124 + 17; hence not 59 divides 7333 by NAT_4:9;
    7333 = 61*120 + 13; hence not 61 divides 7333 by NAT_4:9;
    7333 = 67*109 + 30; hence not 67 divides 7333 by NAT_4:9;
    7333 = 71*103 + 20; hence not 71 divides 7333 by NAT_4:9;
    7333 = 73*100 + 33; hence not 73 divides 7333 by NAT_4:9;
    7333 = 79*92 + 65; hence not 79 divides 7333 by NAT_4:9;
    7333 = 83*88 + 29; hence not 83 divides 7333 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7333 & n is prime
  holds not n divides 7333 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
