Prime or composite?

ok so i checked an online prime number checker and it said it is prime

well, to work out if 1,111,111,111,111,177,777,777,777 is a prime number, we find the square root of it and round it up (so if you have 11.3 round it up to 12) then see if any primes below that number divide into it (i have a bad feeling about this). sqrt(1,111,111,111,111,177,777,777,777)=1054092553389.491 rounded up is 1054092553390. Then i give up and let my brain solidify again and take a nap 

Using Miller–Rabin primality test, it shows that  11 11 11 11 11 11 11 7 7 7 7 7 7 7 7 7 7 7 is a PRIME number!. It can also be written as the SUM of two squares as follows:

n = a² + b²

a = 1,053,802,513,824

b = 24,725,957,401