# Can it be proven that infinite many primes can be formed only using two distinct digits?

It seems obvious that infinite many primes can be formed only using two distinct digits.

$67776767776667777777$ is an example for such a prime. Even if we allow only the digits $0$ and $1$, there are $2^{n-2}$ numbers with $n$ digits, for which the first and last digit is $1$. So, we can expect that some of those numbers are prime for every sufficiently large number $n$.

Can it be proven that infinite many primes contain only two distinct digits in the decimal representation ?

• Similar questioh at math.stackexchange.com/questions/162042/…, which is answered by GerryMyerson: the status is not known. – Aravind Nov 24 '15 at 14:49
• Thank you for pointing out this very negative result. – Peter Nov 24 '15 at 15:44
• I recommend you set up an Internet alert on this page: oeis.org/A020469 – Robert Soupe Nov 27 '15 at 18:24