Three conjecture on the primes obtained concatenating p with (p-1)/2 respectively with (p+1)/2 where p prime

In this paper I make the following three conjectures on primes: (I) there exist an infinity of primes q obtained concatenating to the left a prime p with the number (p – 1)/2 (example: for p = 23, q is the number obtained concatenating 23 to the left with (p – 1)/2 = 11, i.e. q = 1123, prime); (II) there exist an infinity of primes q obtained concatenating to the left a prime p with the number (p + 1)/2 (example: for p = 41, q is the number obtained concatenating 41 to the left with (p + 1)/2 = 21, i.e. q = 2141, prime); (III) there exist an infinity of pairs of primes (q1, q2) where q1 is obtained concatenating to the left a prime p with the number (p – 1)/2 and q2 is obtained concatenating to the left the same prime p with the number (p + 1)/2.