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A factorial x! is the product of all numbers from 1 to x. The first: 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600 (sequence A000142 in the OEIS). 0! = 1 is sometimes included. A k-smooth number (for a natural number k) has its prime factors ≤ k (so it is also j-smooth for any j > k). m is smoother than n if the ...
As 120 is a factorial and one less than a square (! =), it—with 11—is one of the few Brown number pairs. 120 appears in Pierre de Fermat's modified Diophantine problem as the largest known integer of the sequence 1, 3, 8, 120. Fermat wanted to find another positive integer that, when multiplied by any of the other numbers in the sequence ...
In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind. For example, 3 × 5 is an integer factorization of 15, and (x – 2)(x + 2) is a polynomial ...
For example, 15 is a composite number because 15 = 3 · 5, but 7 is a prime number because it cannot be decomposed in this way. If one of the factors is composite, it can in turn be written as a product of smaller factors, for example 60 = 3 · 20 = 3 · (5 · 4) .
As of December 2019 the largest number known to have been factored by a general-purpose algorithm is RSA-240, which has 240 decimal digits (795 bits) and is the product of two large primes. [155] Shor's algorithm can factor any integer in a polynomial number of steps on a quantum computer. [156]
Today's NYT Connections puzzle for Wednesday, January 15, 2025The New York Times
However, amicable numbers where the two members have different smallest prime factors do exist: there are seven such pairs known. [8] Also, every known pair shares at least one common prime factor . It is not known whether a pair of coprime amicable numbers exists, though if any does, the product of the two must be greater than 10 65 .
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