Is finding prime factors an NP problem?

Is finding prime factors an NP problem?

The prime factorization problem is in the NP class, but we don’t know if it is NP-hard. In other words, there is currently no proof that prime factorization problem cannot be solved polynomial time (= in P).

Is prime Factorisation NP hard?

Difficulty and complexity The problem is clearly in class NP, but it is generally suspected that it is not NP-complete, though this has not been proven. For current computers, GNFS is the best published algorithm for large n (more than about 400 bits).

Why is factoring in NP?

It is in NP, because a factor p. It is in co-NP because a prime factorization of n with no factors

Is Prime NP-complete?

No, unless P turns out to be equal to NP. I’m not sure if it will be NP complete even then. primality-proving algorithm created and published by Manindra Agrawal , Neeraj Kayal , and Nitin Saxena , computer scientists at the Indian Institute of Technology Kanpur , on August 6, 2002, in a paper titled “PRIMES is in P”.

Is factoring a hard problem?

Factoring integers into prime factors has a reputation as an extraordinarily difficult problem. Enough people have tried to find efficient factoring algorithms that we can be confident the problem isn’t easy, but there’s no reason to think it’s impossible. …

Is prime NP complete?

Why is it so hard to factor large numbers into primes?

First off: factoring numbers, large and small, into primes is not a hard problem. It’s a trivial problem. Given a number, you can successively search for its divisors until it’s completely factored. That’s guaranteed to work and take up a finite amount of time, which quite naturally grows with the size of the number you are trying to factor.

What is prime factorization and prime factors?

Prime factorization is a process of factoring a number in terms of prime numbers i.e. the factors will be prime numbers. Here, all the concepts of prime factors and prime factorization methods have been explained which will help the students understand how to find the prime factors of a number easily.

How do you find the factors of a non-prime number?

There is only one possible way to determine the factors of a non-prime number, and that is to try dividing it by all possible factors. You can make this a little more efficient by only trying prime factors, and you only need to go up to the square root of the number, but the fact remains: we are going to have to do a lot of division.

Why is factorization so hard?

When people say “factorization is hard”, they mean that there’s no efficient algorithm for factorization, and “efficient” means “one that requires shockingly less time than you would expect for a problem of this size”. I’m not using “shockingly” lightly here.