The probability that any exponent is a prime is the Proth Weight for the k value divided by ln(x). This is the prime number theorem weight adjusted for the unusual divisibility properties of Proth numbers - things like none are divisibly by 2 and 1/2 are divisibly by 3 instead of 1/2 and 1/3. Yves Gallot has Proth weights in Table 5 of this paper.Originally posted by Keroberts1
I know the question has been asked before but i wasn't sure if anyone was ever able to figure it out. Does anyone know what the probability of a certain N value turning out to be prime, and where is the current 50% line for when we'll find the next prime. I'm just trying ot figure out if this is a DC project I can hope to see finish in my life time.
Adding up all the weights for all the exponents, there is a 50% chance of at least one prime between 4.2M and 5.4M.