
theorem
  9769 is prime
proof
  now
    9769 = 2*4884 + 1; hence not 2 divides 9769 by NAT_4:9;
    9769 = 3*3256 + 1; hence not 3 divides 9769 by NAT_4:9;
    9769 = 5*1953 + 4; hence not 5 divides 9769 by NAT_4:9;
    9769 = 7*1395 + 4; hence not 7 divides 9769 by NAT_4:9;
    9769 = 11*888 + 1; hence not 11 divides 9769 by NAT_4:9;
    9769 = 13*751 + 6; hence not 13 divides 9769 by NAT_4:9;
    9769 = 17*574 + 11; hence not 17 divides 9769 by NAT_4:9;
    9769 = 19*514 + 3; hence not 19 divides 9769 by NAT_4:9;
    9769 = 23*424 + 17; hence not 23 divides 9769 by NAT_4:9;
    9769 = 29*336 + 25; hence not 29 divides 9769 by NAT_4:9;
    9769 = 31*315 + 4; hence not 31 divides 9769 by NAT_4:9;
    9769 = 37*264 + 1; hence not 37 divides 9769 by NAT_4:9;
    9769 = 41*238 + 11; hence not 41 divides 9769 by NAT_4:9;
    9769 = 43*227 + 8; hence not 43 divides 9769 by NAT_4:9;
    9769 = 47*207 + 40; hence not 47 divides 9769 by NAT_4:9;
    9769 = 53*184 + 17; hence not 53 divides 9769 by NAT_4:9;
    9769 = 59*165 + 34; hence not 59 divides 9769 by NAT_4:9;
    9769 = 61*160 + 9; hence not 61 divides 9769 by NAT_4:9;
    9769 = 67*145 + 54; hence not 67 divides 9769 by NAT_4:9;
    9769 = 71*137 + 42; hence not 71 divides 9769 by NAT_4:9;
    9769 = 73*133 + 60; hence not 73 divides 9769 by NAT_4:9;
    9769 = 79*123 + 52; hence not 79 divides 9769 by NAT_4:9;
    9769 = 83*117 + 58; hence not 83 divides 9769 by NAT_4:9;
    9769 = 89*109 + 68; hence not 89 divides 9769 by NAT_4:9;
    9769 = 97*100 + 69; hence not 97 divides 9769 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9769 & n is prime
  holds not n divides 9769 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
