
theorem
  9743 is prime
proof
  now
    9743 = 2*4871 + 1; hence not 2 divides 9743 by NAT_4:9;
    9743 = 3*3247 + 2; hence not 3 divides 9743 by NAT_4:9;
    9743 = 5*1948 + 3; hence not 5 divides 9743 by NAT_4:9;
    9743 = 7*1391 + 6; hence not 7 divides 9743 by NAT_4:9;
    9743 = 11*885 + 8; hence not 11 divides 9743 by NAT_4:9;
    9743 = 13*749 + 6; hence not 13 divides 9743 by NAT_4:9;
    9743 = 17*573 + 2; hence not 17 divides 9743 by NAT_4:9;
    9743 = 19*512 + 15; hence not 19 divides 9743 by NAT_4:9;
    9743 = 23*423 + 14; hence not 23 divides 9743 by NAT_4:9;
    9743 = 29*335 + 28; hence not 29 divides 9743 by NAT_4:9;
    9743 = 31*314 + 9; hence not 31 divides 9743 by NAT_4:9;
    9743 = 37*263 + 12; hence not 37 divides 9743 by NAT_4:9;
    9743 = 41*237 + 26; hence not 41 divides 9743 by NAT_4:9;
    9743 = 43*226 + 25; hence not 43 divides 9743 by NAT_4:9;
    9743 = 47*207 + 14; hence not 47 divides 9743 by NAT_4:9;
    9743 = 53*183 + 44; hence not 53 divides 9743 by NAT_4:9;
    9743 = 59*165 + 8; hence not 59 divides 9743 by NAT_4:9;
    9743 = 61*159 + 44; hence not 61 divides 9743 by NAT_4:9;
    9743 = 67*145 + 28; hence not 67 divides 9743 by NAT_4:9;
    9743 = 71*137 + 16; hence not 71 divides 9743 by NAT_4:9;
    9743 = 73*133 + 34; hence not 73 divides 9743 by NAT_4:9;
    9743 = 79*123 + 26; hence not 79 divides 9743 by NAT_4:9;
    9743 = 83*117 + 32; hence not 83 divides 9743 by NAT_4:9;
    9743 = 89*109 + 42; hence not 89 divides 9743 by NAT_4:9;
    9743 = 97*100 + 43; hence not 97 divides 9743 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9743 & n is prime
  holds not n divides 9743 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
