
theorem
  9497 is prime
proof
  now
    9497 = 2*4748 + 1; hence not 2 divides 9497 by NAT_4:9;
    9497 = 3*3165 + 2; hence not 3 divides 9497 by NAT_4:9;
    9497 = 5*1899 + 2; hence not 5 divides 9497 by NAT_4:9;
    9497 = 7*1356 + 5; hence not 7 divides 9497 by NAT_4:9;
    9497 = 11*863 + 4; hence not 11 divides 9497 by NAT_4:9;
    9497 = 13*730 + 7; hence not 13 divides 9497 by NAT_4:9;
    9497 = 17*558 + 11; hence not 17 divides 9497 by NAT_4:9;
    9497 = 19*499 + 16; hence not 19 divides 9497 by NAT_4:9;
    9497 = 23*412 + 21; hence not 23 divides 9497 by NAT_4:9;
    9497 = 29*327 + 14; hence not 29 divides 9497 by NAT_4:9;
    9497 = 31*306 + 11; hence not 31 divides 9497 by NAT_4:9;
    9497 = 37*256 + 25; hence not 37 divides 9497 by NAT_4:9;
    9497 = 41*231 + 26; hence not 41 divides 9497 by NAT_4:9;
    9497 = 43*220 + 37; hence not 43 divides 9497 by NAT_4:9;
    9497 = 47*202 + 3; hence not 47 divides 9497 by NAT_4:9;
    9497 = 53*179 + 10; hence not 53 divides 9497 by NAT_4:9;
    9497 = 59*160 + 57; hence not 59 divides 9497 by NAT_4:9;
    9497 = 61*155 + 42; hence not 61 divides 9497 by NAT_4:9;
    9497 = 67*141 + 50; hence not 67 divides 9497 by NAT_4:9;
    9497 = 71*133 + 54; hence not 71 divides 9497 by NAT_4:9;
    9497 = 73*130 + 7; hence not 73 divides 9497 by NAT_4:9;
    9497 = 79*120 + 17; hence not 79 divides 9497 by NAT_4:9;
    9497 = 83*114 + 35; hence not 83 divides 9497 by NAT_4:9;
    9497 = 89*106 + 63; hence not 89 divides 9497 by NAT_4:9;
    9497 = 97*97 + 88; hence not 97 divides 9497 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9497 & n is prime
  holds not n divides 9497 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
