
theorem
  7297 is prime
proof
  now
    7297 = 2*3648 + 1; hence not 2 divides 7297 by NAT_4:9;
    7297 = 3*2432 + 1; hence not 3 divides 7297 by NAT_4:9;
    7297 = 5*1459 + 2; hence not 5 divides 7297 by NAT_4:9;
    7297 = 7*1042 + 3; hence not 7 divides 7297 by NAT_4:9;
    7297 = 11*663 + 4; hence not 11 divides 7297 by NAT_4:9;
    7297 = 13*561 + 4; hence not 13 divides 7297 by NAT_4:9;
    7297 = 17*429 + 4; hence not 17 divides 7297 by NAT_4:9;
    7297 = 19*384 + 1; hence not 19 divides 7297 by NAT_4:9;
    7297 = 23*317 + 6; hence not 23 divides 7297 by NAT_4:9;
    7297 = 29*251 + 18; hence not 29 divides 7297 by NAT_4:9;
    7297 = 31*235 + 12; hence not 31 divides 7297 by NAT_4:9;
    7297 = 37*197 + 8; hence not 37 divides 7297 by NAT_4:9;
    7297 = 41*177 + 40; hence not 41 divides 7297 by NAT_4:9;
    7297 = 43*169 + 30; hence not 43 divides 7297 by NAT_4:9;
    7297 = 47*155 + 12; hence not 47 divides 7297 by NAT_4:9;
    7297 = 53*137 + 36; hence not 53 divides 7297 by NAT_4:9;
    7297 = 59*123 + 40; hence not 59 divides 7297 by NAT_4:9;
    7297 = 61*119 + 38; hence not 61 divides 7297 by NAT_4:9;
    7297 = 67*108 + 61; hence not 67 divides 7297 by NAT_4:9;
    7297 = 71*102 + 55; hence not 71 divides 7297 by NAT_4:9;
    7297 = 73*99 + 70; hence not 73 divides 7297 by NAT_4:9;
    7297 = 79*92 + 29; hence not 79 divides 7297 by NAT_4:9;
    7297 = 83*87 + 76; hence not 83 divides 7297 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7297 & n is prime
  holds not n divides 7297 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
