Primes obtained concatenating 30p with 30q then adding or subtracting 1, where p and q=p+6 primes

In this paper I state the following three conjectures: let [p, q] be a pair of sexy primes (q = p + 6); then: (I) there exist an infinity of primes obtained concatenating 30*p with 30*q and adding 1 to the resulted number; example: for [p, q] = [23, 29], the number 690871 is prime; (II) there exist an infinity of primes obtained concatenating 30*p with 30*q and subtracting 1 from the resulted number; example: for [p, q] = [23, 29], the number 690869 is prime; (III) there exist an infinity of pairs of twin primes obtained concatenating 30*p with 30*q and adding/subtracting 1 from the resulted number; example: for [p, q] = [101, 107], the numbers 30303209 and 30303211 are primes.