I assume this market is only about the infinitude of such primes (and not about the density of such primes in the set of all primes).

Reason I'm confident about it being true: it follows from a generalization of the Riemann hypothesis, it also follows from (a special case of) "Schinzel's hypothesis H", and both are widely expected to be true. Some weaker forms about it being true for "most integers" have been proven. And as usual, there's a lot of numerical support.