Doesn't cracking this problem boil down to finding a pattern in prime numbers, which doesn't seem to exist? For the researchers that think the task is efficiently computable in polynomial time, whats the reason behind their thinking?
Some discussion of why some believe factoring could be easy can be found here: [2]
[1] https://en.wikipedia.org/wiki/AKS_primality_test
[2] https://mathoverflow.net/questions/79366/evidence-for-intege...