Three conjectures on twin primes involving the sum of their digits

TL;DRAbstract

Observing the sum of the digits of a number of twin primes, I make in this paper the following three conjectures: (1) for any m the lesser term from a pair of twin primes having as the sum of its digits an odd number there exist an infinity of lesser terms n from pairs of twin primes having as the sum of its digits an even number such that m + n + 1 is prime, (2) for any m the lesser term from a pair of twin primes having as the sum of its digits an even number there exist an infinity of lesser terms n from pairs of twin primes having as the sum of its digits an odd number such that m + n + 1 is prime and (3) if a, b, c, d are four distinct terms of the sequence of lesser from a pair of twin primes and a + b + 1 = c + d + 1 = x, then x is a semiprime, product of twin primes.

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