
theorem
  9677 is prime
proof
  now
    9677 = 2*4838 + 1; hence not 2 divides 9677 by NAT_4:9;
    9677 = 3*3225 + 2; hence not 3 divides 9677 by NAT_4:9;
    9677 = 5*1935 + 2; hence not 5 divides 9677 by NAT_4:9;
    9677 = 7*1382 + 3; hence not 7 divides 9677 by NAT_4:9;
    9677 = 11*879 + 8; hence not 11 divides 9677 by NAT_4:9;
    9677 = 13*744 + 5; hence not 13 divides 9677 by NAT_4:9;
    9677 = 17*569 + 4; hence not 17 divides 9677 by NAT_4:9;
    9677 = 19*509 + 6; hence not 19 divides 9677 by NAT_4:9;
    9677 = 23*420 + 17; hence not 23 divides 9677 by NAT_4:9;
    9677 = 29*333 + 20; hence not 29 divides 9677 by NAT_4:9;
    9677 = 31*312 + 5; hence not 31 divides 9677 by NAT_4:9;
    9677 = 37*261 + 20; hence not 37 divides 9677 by NAT_4:9;
    9677 = 41*236 + 1; hence not 41 divides 9677 by NAT_4:9;
    9677 = 43*225 + 2; hence not 43 divides 9677 by NAT_4:9;
    9677 = 47*205 + 42; hence not 47 divides 9677 by NAT_4:9;
    9677 = 53*182 + 31; hence not 53 divides 9677 by NAT_4:9;
    9677 = 59*164 + 1; hence not 59 divides 9677 by NAT_4:9;
    9677 = 61*158 + 39; hence not 61 divides 9677 by NAT_4:9;
    9677 = 67*144 + 29; hence not 67 divides 9677 by NAT_4:9;
    9677 = 71*136 + 21; hence not 71 divides 9677 by NAT_4:9;
    9677 = 73*132 + 41; hence not 73 divides 9677 by NAT_4:9;
    9677 = 79*122 + 39; hence not 79 divides 9677 by NAT_4:9;
    9677 = 83*116 + 49; hence not 83 divides 9677 by NAT_4:9;
    9677 = 89*108 + 65; hence not 89 divides 9677 by NAT_4:9;
    9677 = 97*99 + 74; hence not 97 divides 9677 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9677 & n is prime
  holds not n divides 9677 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
