Note from Winn: The following is important work from Mark Carney, the math guy behind my latest book, Analogue Network Security.
Grant et al. at BlackHat 2019 will present weak, and potentially fallacious claims about prime numbers in his talk at 1:20pm on Thursday, August 8th. Their methods in the paper  speculatively improve the speed of checking whether numbers are prime or not, with a view to a knock-on effect of speeding up the cracking of cryptographic key material.
The problem with the paper, and indeed the whole outset, is that it is beset by mathematical errors and inaccuracies, as well as a fundamental misunderstanding of the existing results concerning the distribution and occurrence of prime numbers. We present these ideas in the draft . Notably, we give a lower bound function for the general (and non-unique, contrary to Grant’s claims) class of ‘prime checkers/generators’, showing that the best cases are bounded below by an unbounded function.