
theorem
  1297 is prime
proof
  now
    1297 = 2*648 + 1; hence not 2 divides 1297 by NAT_4:9;
    1297 = 3*432 + 1; hence not 3 divides 1297 by NAT_4:9;
    1297 = 5*259 + 2; hence not 5 divides 1297 by NAT_4:9;
    1297 = 7*185 + 2; hence not 7 divides 1297 by NAT_4:9;
    1297 = 11*117 + 10; hence not 11 divides 1297 by NAT_4:9;
    1297 = 13*99 + 10; hence not 13 divides 1297 by NAT_4:9;
    1297 = 17*76 + 5; hence not 17 divides 1297 by NAT_4:9;
    1297 = 19*68 + 5; hence not 19 divides 1297 by NAT_4:9;
    1297 = 23*56 + 9; hence not 23 divides 1297 by NAT_4:9;
    1297 = 29*44 + 21; hence not 29 divides 1297 by NAT_4:9;
    1297 = 31*41 + 26; hence not 31 divides 1297 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1297 & n is prime
  holds not n divides 1297 by XPRIMET1:22;
  hence thesis by NAT_4:14;
end;
