Yes, prime factorization is not an NP-complete problem. It is in fact in the complexity class NP, but it is not known to be NP-complete.
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In mathematical notation, a prime is used to denote a derivative or a different variable, while an apostrophe is used to indicate a prime number.
Yes, the problem is polynomially reducible to another problem if it can be transformed into that problem with a polynomial-time algorithm.
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A problem is a situation that needs to be solved, while an algorithm is a step-by-step procedure for solving a problem. In problem-solving, the problem is the challenge to be addressed, while the algorithm is the specific method used to find a solution to the problem.
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