
theorem
  9767 is prime
proof
  now
    9767 = 2*4883 + 1; hence not 2 divides 9767 by NAT_4:9;
    9767 = 3*3255 + 2; hence not 3 divides 9767 by NAT_4:9;
    9767 = 5*1953 + 2; hence not 5 divides 9767 by NAT_4:9;
    9767 = 7*1395 + 2; hence not 7 divides 9767 by NAT_4:9;
    9767 = 11*887 + 10; hence not 11 divides 9767 by NAT_4:9;
    9767 = 13*751 + 4; hence not 13 divides 9767 by NAT_4:9;
    9767 = 17*574 + 9; hence not 17 divides 9767 by NAT_4:9;
    9767 = 19*514 + 1; hence not 19 divides 9767 by NAT_4:9;
    9767 = 23*424 + 15; hence not 23 divides 9767 by NAT_4:9;
    9767 = 29*336 + 23; hence not 29 divides 9767 by NAT_4:9;
    9767 = 31*315 + 2; hence not 31 divides 9767 by NAT_4:9;
    9767 = 37*263 + 36; hence not 37 divides 9767 by NAT_4:9;
    9767 = 41*238 + 9; hence not 41 divides 9767 by NAT_4:9;
    9767 = 43*227 + 6; hence not 43 divides 9767 by NAT_4:9;
    9767 = 47*207 + 38; hence not 47 divides 9767 by NAT_4:9;
    9767 = 53*184 + 15; hence not 53 divides 9767 by NAT_4:9;
    9767 = 59*165 + 32; hence not 59 divides 9767 by NAT_4:9;
    9767 = 61*160 + 7; hence not 61 divides 9767 by NAT_4:9;
    9767 = 67*145 + 52; hence not 67 divides 9767 by NAT_4:9;
    9767 = 71*137 + 40; hence not 71 divides 9767 by NAT_4:9;
    9767 = 73*133 + 58; hence not 73 divides 9767 by NAT_4:9;
    9767 = 79*123 + 50; hence not 79 divides 9767 by NAT_4:9;
    9767 = 83*117 + 56; hence not 83 divides 9767 by NAT_4:9;
    9767 = 89*109 + 66; hence not 89 divides 9767 by NAT_4:9;
    9767 = 97*100 + 67; hence not 97 divides 9767 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9767 & n is prime
  holds not n divides 9767 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
