reserve a,b,d,n,k,i,j,x,s for Nat;

theorem Th18:
  33331 is prime
proof
  now
    33331 = 2*16665 + 1; hence not 2 divides 33331;
    33331 = 3*11110 + 1; hence not 3 divides 33331 by NAT_4:9;
    33331 = 5*6666 + 1; hence not 5 divides 33331 by NAT_4:9;
    33331 = 7*4761 + 4; hence not 7 divides 33331 by NAT_4:9;
    33331 = 11*3030 + 1; hence not 11 divides 33331 by NAT_4:9;
    33331 = 13*2563 + 12; hence not 13 divides 33331 by NAT_4:9;
    33331 = 17*1960 + 11; hence not 17 divides 33331 by NAT_4:9;
    33331 = 19*1754 + 5; hence not 19 divides 33331 by NAT_4:9;
    33331 = 23*1449 + 4; hence not 23 divides 33331 by NAT_4:9;
    33331 = 29*1149+10; hence not 29 divides 33331 by NAT_4:9;
    33331 = 31*1075+6; hence not 31 divides 33331 by NAT_4:9;
    33331 = 37*900+31; hence not 37 divides 33331 by NAT_4:9;
    33331 = 41*812+39; hence not 41 divides 33331 by NAT_4:9;
    33331 = 43*775+6; hence not 43 divides 33331 by NAT_4:9;
    33331 = 47*709+8; hence not 47 divides 33331 by NAT_4:9;
    33331 = 53*628+47; hence not 53 divides 33331 by NAT_4:9;
    33331 = 59*564+55; hence not 59 divides 33331 by NAT_4:9;
    33331 = 61*546+25; hence not 61 divides 33331 by NAT_4:9;
    33331 = 67*497+32; hence not 67 divides 33331 by NAT_4:9;
    33331 = 71*469+32; hence not 71 divides 33331 by NAT_4:9;
    33331 = 73*456+43; hence not 73 divides 33331 by NAT_4:9;
    33331 = 79*421+72; hence not 79 divides 33331 by NAT_4:9;
    33331 = 83*401+48; hence not 83 divides 33331 by NAT_4:9;
    33331 = 89*374+45; hence not 89 divides 33331 by NAT_4:9;
    33331 = 97*343+60; hence not 97 divides 33331 by NAT_4:9;
    33331 = 101*330+1; hence not 101 divides 33331 by NAT_4:9;
    33331 = 101 * 330 + 1; hence not 101 divides 33331 by NAT_4:9;
    33331 = 103 * 323 + 62; hence not 103 divides 33331 by NAT_4:9;
    33331 = 107 * 311 + 54; hence not 107 divides 33331 by NAT_4:9;
    33331 = 109 * 305 + 86; hence not 109 divides 33331 by NAT_4:9;
    33331 = 113 * 294 + 109; hence not 113 divides 33331 by NAT_4:9;
    33331 = 127 * 262 + 57; hence not 127 divides 33331 by NAT_4:9;
    33331 = 131 * 254 + 57; hence not 131 divides 33331 by NAT_4:9;
    33331 = 137 * 243 + 40; hence not 137 divides 33331 by NAT_4:9;
    33331 = 139 * 239 + 110; hence not 139 divides 33331 by NAT_4:9;
    33331 = 149 * 223 + 104; hence not 149 divides 33331 by NAT_4:9;
    33331 = 151 * 220 + 111; hence not 151 divides 33331 by NAT_4:9;
    33331 = 157 * 212 + 47; hence not 157 divides 33331 by NAT_4:9;
    33331 = 163 * 204 + 79; hence not 163 divides 33331 by NAT_4:9;
    33331 = 167 * 199 + 98; hence not 167 divides 33331 by NAT_4:9;
    33331 = 173 * 192 + 115; hence not 173 divides 33331 by NAT_4:9;
    33331 = 179 * 186 + 37; hence not 179 divides 33331 by NAT_4:9;
    33331 = 181 * 184 + 27; hence not 181 divides 33331 by NAT_4:9;
  end;
  then for n be Element of NAT st 1 < n & n*n <= 33331 & n is prime
  holds not n divides 33331 by XPRIMET1:84;
  hence thesis by NAT_4:14;
end;
