
theorem
  5333 is prime
proof
  now
    5333 = 2*2666 + 1; hence not 2 divides 5333 by NAT_4:9;
    5333 = 3*1777 + 2; hence not 3 divides 5333 by NAT_4:9;
    5333 = 5*1066 + 3; hence not 5 divides 5333 by NAT_4:9;
    5333 = 7*761 + 6; hence not 7 divides 5333 by NAT_4:9;
    5333 = 11*484 + 9; hence not 11 divides 5333 by NAT_4:9;
    5333 = 13*410 + 3; hence not 13 divides 5333 by NAT_4:9;
    5333 = 17*313 + 12; hence not 17 divides 5333 by NAT_4:9;
    5333 = 19*280 + 13; hence not 19 divides 5333 by NAT_4:9;
    5333 = 23*231 + 20; hence not 23 divides 5333 by NAT_4:9;
    5333 = 29*183 + 26; hence not 29 divides 5333 by NAT_4:9;
    5333 = 31*172 + 1; hence not 31 divides 5333 by NAT_4:9;
    5333 = 37*144 + 5; hence not 37 divides 5333 by NAT_4:9;
    5333 = 41*130 + 3; hence not 41 divides 5333 by NAT_4:9;
    5333 = 43*124 + 1; hence not 43 divides 5333 by NAT_4:9;
    5333 = 47*113 + 22; hence not 47 divides 5333 by NAT_4:9;
    5333 = 53*100 + 33; hence not 53 divides 5333 by NAT_4:9;
    5333 = 59*90 + 23; hence not 59 divides 5333 by NAT_4:9;
    5333 = 61*87 + 26; hence not 61 divides 5333 by NAT_4:9;
    5333 = 67*79 + 40; hence not 67 divides 5333 by NAT_4:9;
    5333 = 71*75 + 8; hence not 71 divides 5333 by NAT_4:9;
    5333 = 73*73 + 4; hence not 73 divides 5333 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5333 & n is prime
  holds not n divides 5333 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
