Three conjecture on the numbers obtained concatenating p^2 with (p^2+1)/2, p+12, p^2+12

In this paper I make the following three conjectures on squares of primes: (I) there exist an infinity of primes q obtained concatenating to the left a square of a prime p^2 with the number (p^2 + 1)/2 (example: for p = 17, p^2 = 289 and q is the number obtained concatenating 289 to the left with (p^2 + 1)/2 = 145, i.e. q = 145289, prime); (II) there exist an infinity of primes q obtained concatenating to the left a square of a prime p^2 with the number p + 12 (example: for p = 7, p^2 = 49 and q = 1949, prime); (III) there exist an infinity of primes q obtained concatenating to the left a square of a prime p^2 with the number p^ + 12 (example: for p = 11, p^2 = 121 and q = 133121, prime).