
theorem
  9781 is prime
proof
  now
    9781 = 2*4890 + 1; hence not 2 divides 9781 by NAT_4:9;
    9781 = 3*3260 + 1; hence not 3 divides 9781 by NAT_4:9;
    9781 = 5*1956 + 1; hence not 5 divides 9781 by NAT_4:9;
    9781 = 7*1397 + 2; hence not 7 divides 9781 by NAT_4:9;
    9781 = 11*889 + 2; hence not 11 divides 9781 by NAT_4:9;
    9781 = 13*752 + 5; hence not 13 divides 9781 by NAT_4:9;
    9781 = 17*575 + 6; hence not 17 divides 9781 by NAT_4:9;
    9781 = 19*514 + 15; hence not 19 divides 9781 by NAT_4:9;
    9781 = 23*425 + 6; hence not 23 divides 9781 by NAT_4:9;
    9781 = 29*337 + 8; hence not 29 divides 9781 by NAT_4:9;
    9781 = 31*315 + 16; hence not 31 divides 9781 by NAT_4:9;
    9781 = 37*264 + 13; hence not 37 divides 9781 by NAT_4:9;
    9781 = 41*238 + 23; hence not 41 divides 9781 by NAT_4:9;
    9781 = 43*227 + 20; hence not 43 divides 9781 by NAT_4:9;
    9781 = 47*208 + 5; hence not 47 divides 9781 by NAT_4:9;
    9781 = 53*184 + 29; hence not 53 divides 9781 by NAT_4:9;
    9781 = 59*165 + 46; hence not 59 divides 9781 by NAT_4:9;
    9781 = 61*160 + 21; hence not 61 divides 9781 by NAT_4:9;
    9781 = 67*145 + 66; hence not 67 divides 9781 by NAT_4:9;
    9781 = 71*137 + 54; hence not 71 divides 9781 by NAT_4:9;
    9781 = 73*133 + 72; hence not 73 divides 9781 by NAT_4:9;
    9781 = 79*123 + 64; hence not 79 divides 9781 by NAT_4:9;
    9781 = 83*117 + 70; hence not 83 divides 9781 by NAT_4:9;
    9781 = 89*109 + 80; hence not 89 divides 9781 by NAT_4:9;
    9781 = 97*100 + 81; hence not 97 divides 9781 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9781 & n is prime
  holds not n divides 9781 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
