Three Conjectures on the Numbers Obtained Concatenating the Multiples of 30 with the Squares of Primes

In this paper I conjecture that there exist an infinity of numbers ab formed by concatenation from a multiple of 30, a, and a square of a prime, b, which are primes or powers of primes, respectively semiprimes p*q such that q – p + 1 is prime or power of prime, respectively semiprimes p1*q1 such that q1 – p1 + 1 is semiprime p2*q2 such that q2 – p2 + 1 is prime or power of prime.