
theorem
  5303 is prime
proof
  now
    5303 = 2*2651 + 1; hence not 2 divides 5303 by NAT_4:9;
    5303 = 3*1767 + 2; hence not 3 divides 5303 by NAT_4:9;
    5303 = 5*1060 + 3; hence not 5 divides 5303 by NAT_4:9;
    5303 = 7*757 + 4; hence not 7 divides 5303 by NAT_4:9;
    5303 = 11*482 + 1; hence not 11 divides 5303 by NAT_4:9;
    5303 = 13*407 + 12; hence not 13 divides 5303 by NAT_4:9;
    5303 = 17*311 + 16; hence not 17 divides 5303 by NAT_4:9;
    5303 = 19*279 + 2; hence not 19 divides 5303 by NAT_4:9;
    5303 = 23*230 + 13; hence not 23 divides 5303 by NAT_4:9;
    5303 = 29*182 + 25; hence not 29 divides 5303 by NAT_4:9;
    5303 = 31*171 + 2; hence not 31 divides 5303 by NAT_4:9;
    5303 = 37*143 + 12; hence not 37 divides 5303 by NAT_4:9;
    5303 = 41*129 + 14; hence not 41 divides 5303 by NAT_4:9;
    5303 = 43*123 + 14; hence not 43 divides 5303 by NAT_4:9;
    5303 = 47*112 + 39; hence not 47 divides 5303 by NAT_4:9;
    5303 = 53*100 + 3; hence not 53 divides 5303 by NAT_4:9;
    5303 = 59*89 + 52; hence not 59 divides 5303 by NAT_4:9;
    5303 = 61*86 + 57; hence not 61 divides 5303 by NAT_4:9;
    5303 = 67*79 + 10; hence not 67 divides 5303 by NAT_4:9;
    5303 = 71*74 + 49; hence not 71 divides 5303 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5303 & n is prime
  holds not n divides 5303 by XPRIMET1:40;
  hence thesis by NAT_4:14;
end;
