
theorem
  9649 is prime
proof
  now
    9649 = 2*4824 + 1; hence not 2 divides 9649 by NAT_4:9;
    9649 = 3*3216 + 1; hence not 3 divides 9649 by NAT_4:9;
    9649 = 5*1929 + 4; hence not 5 divides 9649 by NAT_4:9;
    9649 = 7*1378 + 3; hence not 7 divides 9649 by NAT_4:9;
    9649 = 11*877 + 2; hence not 11 divides 9649 by NAT_4:9;
    9649 = 13*742 + 3; hence not 13 divides 9649 by NAT_4:9;
    9649 = 17*567 + 10; hence not 17 divides 9649 by NAT_4:9;
    9649 = 19*507 + 16; hence not 19 divides 9649 by NAT_4:9;
    9649 = 23*419 + 12; hence not 23 divides 9649 by NAT_4:9;
    9649 = 29*332 + 21; hence not 29 divides 9649 by NAT_4:9;
    9649 = 31*311 + 8; hence not 31 divides 9649 by NAT_4:9;
    9649 = 37*260 + 29; hence not 37 divides 9649 by NAT_4:9;
    9649 = 41*235 + 14; hence not 41 divides 9649 by NAT_4:9;
    9649 = 43*224 + 17; hence not 43 divides 9649 by NAT_4:9;
    9649 = 47*205 + 14; hence not 47 divides 9649 by NAT_4:9;
    9649 = 53*182 + 3; hence not 53 divides 9649 by NAT_4:9;
    9649 = 59*163 + 32; hence not 59 divides 9649 by NAT_4:9;
    9649 = 61*158 + 11; hence not 61 divides 9649 by NAT_4:9;
    9649 = 67*144 + 1; hence not 67 divides 9649 by NAT_4:9;
    9649 = 71*135 + 64; hence not 71 divides 9649 by NAT_4:9;
    9649 = 73*132 + 13; hence not 73 divides 9649 by NAT_4:9;
    9649 = 79*122 + 11; hence not 79 divides 9649 by NAT_4:9;
    9649 = 83*116 + 21; hence not 83 divides 9649 by NAT_4:9;
    9649 = 89*108 + 37; hence not 89 divides 9649 by NAT_4:9;
    9649 = 97*99 + 46; hence not 97 divides 9649 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9649 & n is prime
  holds not n divides 9649 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
