Fastest prime factorization algorithm

The fastest-known fully proven deterministic algorithm is the Pollard-Strassen method (Pomerance 1982; Hardy et al. 1990).

1. Is there an algorithm for prime factorization?
2. What is the fastest way to factor large numbers?
3. Is prime factorization NP-hard?
4. Why time complexity is the prime factor for designing an algorithm?

Is there an algorithm for prime factorization?

Algorithm for Prime Factorization

The simplest algorithm to find the prime-factor is by repeatedly dividing the number with the prime factor until the number becomes 1. Thus 100 divided by 2 become 50. Now our number becomes 50. Thus 50 divided by 2 become 25.

What is the fastest way to factor large numbers?

How to Find Factors of Large Numbers? To calculate the factors of large numbers, divide the numbers with the least prime number, i.e. 2. If the number is not divisible by 2, move to the next prime numbers, i.e. 3 and so on until 1 is reached. Below is an example to find the factors of a large number.

Is prime factorization NP-hard?

Integer factorization is not NP-hard (so not NP-complete). (This isn't proven, but it's generally thought to be the case.) So, while doing a polynomial-time integer factorization would be hugely significant (and make all asymmetric encryption in the world useless), it would not prove P=NP.

Why time complexity is the prime factor for designing an algorithm?

The time complexity is the number of operations an algorithm performs to complete its task with respect to input size (considering that each operation takes the same amount of time). The algorithm that performs the task in the smallest number of operations is considered the most efficient one.