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Q: What is the prime fartorization list?

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That's an unfortunate term. The answer to the prime factorization of 56 is 2 x 2 x 2 x 7.

2 x 2 x 2 x 5 = 40

474 237,2 79,3,2

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It is a list of prime numbers.

The list of prime numbers is infinite. There are two factors for each.

That's an infinite list.

The list is far too long to list here (millions of them); a search on "list of prime numbers" can quickly give you the desired prime numbers.

That's an infinite list.

That's an infinite list.

The proof that there is no largest prime:Assume that there are a finite number of primes for the sake of contradiction. Then, there should be a number P that equals p1p2p3...pn+1. P is either prime or not prime (composite). If it is prime, we just show that P is larger than the largest prime in the list. If it's not prime, it must be composite. Composite always has at least one factor that is prime, but since P is not divisible by any prime in the list, the unknown prime factor(s) must be something not in the list, this also shows that there is a prime larger than the largest prime in the list. Both cases show that no matter how large a list of prime numbers, there will be always at least one larger prime outside of that list.

list the prime numbers between one and twenty

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