I am interested in the complexity theoretic equivalences of prime number factorization. My interest stems from prime number factorization being one of the few candidates for NPI.

I am especially interested to learn wether there are some not initially obvious reductions. Any possible reduction type (Karp, Turing, ...) would be of interest. Im sure there is a lot known already on the subject but i am not sure where to find a good resource on this.

I am aware that PRIME, (i.e. the decision problem that checks wheter a number is prime or not), is in $P$. However, i am interested in the harder problem of finding the explicit factorization, which is in $FNP$. This problem is not known to be in $P$ or $NP-complete$ making it a very interesting candidate for $NPI$ problems. Consequently, any reduction would be interesting for understanding $NPI$

Is there a review article or even better a database that comprehensively lists all known reductions to and from prime number factorization?



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