Them four primes This is not a problem from any text, but a curiosity into the pattern of prime numbers.
It is known that 11, 13, 17, 19 are primes.
It is also known that 101, 103, 107, 109 are primes.
Is there any other pair of twin primes, that occur for the unit digit 1, 3, 7, 9 and the same preceding digits of the number? If yes, are they finite or infinite? Is there any pattern or logic to find them?

These are sometimes called prime decades, and they represent the totality of prime quadruplets with the exception of $\{5,7,11,13\}$. See also OEIS A007530.
It is unknown whether or not there are infinitely many. Certainly we don't have a proof of there being infinitely many, because that would imply the twin prime conjecture.
