Integer factorization is currently not known to be NP complete, and is expected to not be so. Therefore, even such a breakthrough as posited in the article would have no immediate bearing on the question of P vs NP.
And a breakthrough in P?=NP could have implications for factorization.
Indeed, but what's implied in the article is that they might have made a breakthrough in factorization specifically, not in fundamental CS theory at large.
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Integer factorization is currently not known to be NP complete, and is expected to not be so. Therefore, even such a breakthrough as posited in the article would have no immediate bearing on the question of P vs NP.
http://en.wikipedia.org/wiki/Integer_factorization#Difficult...
Other way round, multiplication is in P, so integer factorization is in NP. And a breakthrough in P?=NP could have implications for factorization.
I never said it wasn't.
Indeed, but what's implied in the article is that they might have made a breakthrough in factorization specifically, not in fundamental CS theory at large.