Repunit Primes

Write the digit “1” exactly 317 times, and you get a palindromic prime number. Moreover, 317 itself is a prime number!

Primes with 1s

Are there other examples, other than the trivial 11, of primes made of only 1’s? The first known repunit primes of the form (10 – 1)/9 are: 11, 1111111111111111111, 11111111111111111111111, 1 repeated 317 times (as shown above), 1 repeated 1031 times, 1 repeated 49081 times, 1 repeated 270343 times, and so on, … It seems they are infinite. Or not?