
theorem
  9679 is prime
proof
  now
    9679 = 2*4839 + 1; hence not 2 divides 9679 by NAT_4:9;
    9679 = 3*3226 + 1; hence not 3 divides 9679 by NAT_4:9;
    9679 = 5*1935 + 4; hence not 5 divides 9679 by NAT_4:9;
    9679 = 7*1382 + 5; hence not 7 divides 9679 by NAT_4:9;
    9679 = 11*879 + 10; hence not 11 divides 9679 by NAT_4:9;
    9679 = 13*744 + 7; hence not 13 divides 9679 by NAT_4:9;
    9679 = 17*569 + 6; hence not 17 divides 9679 by NAT_4:9;
    9679 = 19*509 + 8; hence not 19 divides 9679 by NAT_4:9;
    9679 = 23*420 + 19; hence not 23 divides 9679 by NAT_4:9;
    9679 = 29*333 + 22; hence not 29 divides 9679 by NAT_4:9;
    9679 = 31*312 + 7; hence not 31 divides 9679 by NAT_4:9;
    9679 = 37*261 + 22; hence not 37 divides 9679 by NAT_4:9;
    9679 = 41*236 + 3; hence not 41 divides 9679 by NAT_4:9;
    9679 = 43*225 + 4; hence not 43 divides 9679 by NAT_4:9;
    9679 = 47*205 + 44; hence not 47 divides 9679 by NAT_4:9;
    9679 = 53*182 + 33; hence not 53 divides 9679 by NAT_4:9;
    9679 = 59*164 + 3; hence not 59 divides 9679 by NAT_4:9;
    9679 = 61*158 + 41; hence not 61 divides 9679 by NAT_4:9;
    9679 = 67*144 + 31; hence not 67 divides 9679 by NAT_4:9;
    9679 = 71*136 + 23; hence not 71 divides 9679 by NAT_4:9;
    9679 = 73*132 + 43; hence not 73 divides 9679 by NAT_4:9;
    9679 = 79*122 + 41; hence not 79 divides 9679 by NAT_4:9;
    9679 = 83*116 + 51; hence not 83 divides 9679 by NAT_4:9;
    9679 = 89*108 + 67; hence not 89 divides 9679 by NAT_4:9;
    9679 = 97*99 + 76; hence not 97 divides 9679 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9679 & n is prime
  holds not n divides 9679 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
