Primes obtained concatenating p-1 with q^2 where p and q are primes or Poulet numbers

In this paper I make the following eight conjectures: (Ia) for any p prime, p > 3, there exist an infinity of primes q such that the number n obtained concatenating p – 1 to the right with q^2 is prime; (Ib) there exist an infinity of terms in any of the sequences above (for any p) such that r = (p – 1)*q^2 + 1 is prime; (IIa) for any q prime, q > 3, there exist an infinity of primes p such that the number n obtained concatenating q^2 to the left with p – 1 is prime; (IIb) there exist an infinity of terms in any of the sequences above (for any q) such that r = (p – 1)*q^2 + 1 is prime; (IIIa) for any Poulet number P, not divisible by 3, there exist an infinity of primes q such that the number n obtained concatenating P – 1 to the right with q^2 is prime; (IIIb) there exist an infinity of terms in any of the sequences above (for any P) such that r = (P – 1)*q^2 + 1 is prime; (IVa) for any Poulet number Q, not divisible by 3 or 5, there exist an infinity of primes p such that the number n obtained concatenating Q^2 to the left with p - 1 is prime; (IVb) there exist an infinity of terms in any of the sequences above (for any Q) such that r = (p – 1)*Q^2 + 1 is prime.