[joantune]

I wonder what the implications are for cryptography - given the heavy reliance on 'random' prime numbers

but one would have to delve into this - and from the top of my head there are no algorithms that make you pick 'two consecutive' primes - so the implications - if any - aren't obvious - anyone here has some more light or other angles to shed into this?

[foo101]

Why would this have any implications on cryptography? This does not make factoring an RSA modules any easier.

[joantune]

Well, in RSA you have to choose two prime numbers, multiply them, and keep them secret. p and q: pq =n . And n is made public. I wonder if this probability, maybe coupled with concrete implementations, makes it for a more restricted set of guessing p and q. That would be it. I guess that given that this only introduces 'restrictions' on sequential prime numbers, doesn't really help at all, given that p and q should be random. Unless there's a shortcut applied in implementation that you find a random p and then q is the next prime number. Hence my question to the community. But I only know that both RSA and DH rely on prime numbers.

[foo101]

That's a fair point. Yes, I thought the same thing too when I read this. It is only introducing restrictions on sequential prime numbers. I doubt it has any bearing on the factoring problem yet, at least not without more work that can connect this to the factoring problem.