- Is factoring in P? (it is known that prime testing is in P; thus the factoring is in NP ∪ coNP) - if it were true, RSA would be broken immediately (and some expert that I talked to told me, he believes that such a factoring algorithm could probably be extended to break ECC, too)
- Goldbach's weak conjecture (http://en.wikipedia.org/wiki/Goldbach%27s_weak_conjecture) - Harald Helfgott claims that he proved it
- Is factoring in P? (it is known that prime testing is in P; thus the factoring is in NP ∪ coNP) - if it were true, RSA would be broken immediately (and some expert that I talked to told me, he believes that such a factoring algorithm could probably be extended to break ECC, too)
- Riemann hypothesis (http://en.wikipedia.org/wiki/Riemann_hypothesis)
- Do for each even number n exist two prime numbers p > q such that n = p-q?