
theorem
  8969 is prime
proof
  now
    8969 = 2*4484 + 1; hence not 2 divides 8969 by NAT_4:9;
    8969 = 3*2989 + 2; hence not 3 divides 8969 by NAT_4:9;
    8969 = 5*1793 + 4; hence not 5 divides 8969 by NAT_4:9;
    8969 = 7*1281 + 2; hence not 7 divides 8969 by NAT_4:9;
    8969 = 11*815 + 4; hence not 11 divides 8969 by NAT_4:9;
    8969 = 13*689 + 12; hence not 13 divides 8969 by NAT_4:9;
    8969 = 17*527 + 10; hence not 17 divides 8969 by NAT_4:9;
    8969 = 19*472 + 1; hence not 19 divides 8969 by NAT_4:9;
    8969 = 23*389 + 22; hence not 23 divides 8969 by NAT_4:9;
    8969 = 29*309 + 8; hence not 29 divides 8969 by NAT_4:9;
    8969 = 31*289 + 10; hence not 31 divides 8969 by NAT_4:9;
    8969 = 37*242 + 15; hence not 37 divides 8969 by NAT_4:9;
    8969 = 41*218 + 31; hence not 41 divides 8969 by NAT_4:9;
    8969 = 43*208 + 25; hence not 43 divides 8969 by NAT_4:9;
    8969 = 47*190 + 39; hence not 47 divides 8969 by NAT_4:9;
    8969 = 53*169 + 12; hence not 53 divides 8969 by NAT_4:9;
    8969 = 59*152 + 1; hence not 59 divides 8969 by NAT_4:9;
    8969 = 61*147 + 2; hence not 61 divides 8969 by NAT_4:9;
    8969 = 67*133 + 58; hence not 67 divides 8969 by NAT_4:9;
    8969 = 71*126 + 23; hence not 71 divides 8969 by NAT_4:9;
    8969 = 73*122 + 63; hence not 73 divides 8969 by NAT_4:9;
    8969 = 79*113 + 42; hence not 79 divides 8969 by NAT_4:9;
    8969 = 83*108 + 5; hence not 83 divides 8969 by NAT_4:9;
    8969 = 89*100 + 69; hence not 89 divides 8969 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8969 & n is prime
  holds not n divides 8969 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
