
theorem
  9749 is prime
proof
  now
    9749 = 2*4874 + 1; hence not 2 divides 9749 by NAT_4:9;
    9749 = 3*3249 + 2; hence not 3 divides 9749 by NAT_4:9;
    9749 = 5*1949 + 4; hence not 5 divides 9749 by NAT_4:9;
    9749 = 7*1392 + 5; hence not 7 divides 9749 by NAT_4:9;
    9749 = 11*886 + 3; hence not 11 divides 9749 by NAT_4:9;
    9749 = 13*749 + 12; hence not 13 divides 9749 by NAT_4:9;
    9749 = 17*573 + 8; hence not 17 divides 9749 by NAT_4:9;
    9749 = 19*513 + 2; hence not 19 divides 9749 by NAT_4:9;
    9749 = 23*423 + 20; hence not 23 divides 9749 by NAT_4:9;
    9749 = 29*336 + 5; hence not 29 divides 9749 by NAT_4:9;
    9749 = 31*314 + 15; hence not 31 divides 9749 by NAT_4:9;
    9749 = 37*263 + 18; hence not 37 divides 9749 by NAT_4:9;
    9749 = 41*237 + 32; hence not 41 divides 9749 by NAT_4:9;
    9749 = 43*226 + 31; hence not 43 divides 9749 by NAT_4:9;
    9749 = 47*207 + 20; hence not 47 divides 9749 by NAT_4:9;
    9749 = 53*183 + 50; hence not 53 divides 9749 by NAT_4:9;
    9749 = 59*165 + 14; hence not 59 divides 9749 by NAT_4:9;
    9749 = 61*159 + 50; hence not 61 divides 9749 by NAT_4:9;
    9749 = 67*145 + 34; hence not 67 divides 9749 by NAT_4:9;
    9749 = 71*137 + 22; hence not 71 divides 9749 by NAT_4:9;
    9749 = 73*133 + 40; hence not 73 divides 9749 by NAT_4:9;
    9749 = 79*123 + 32; hence not 79 divides 9749 by NAT_4:9;
    9749 = 83*117 + 38; hence not 83 divides 9749 by NAT_4:9;
    9749 = 89*109 + 48; hence not 89 divides 9749 by NAT_4:9;
    9749 = 97*100 + 49; hence not 97 divides 9749 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9749 & n is prime
  holds not n divides 9749 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
