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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) .
Every composite number can be written as the product of two or more (not necessarily distinct) primes. [2] For example, the composite number 299 can be written as 13 × 23, and the composite number 360 can be written as 2 3 × 3 2 × 5; furthermore, this representation is unique up to the order of the factors.
4, 728, 73615, 4463535, 15966114, 2050918644, 164736913905, ... (sequence A059754 in the OEIS). Smith numbers can be constructed from factored repunits. [5] [verification needed] As of 2010, the largest known Smith number in base 10 is 9 × R 1031 × (10 4594 + 3 × 10 2297 + 1) 1476 × 10 3 913 210. where R 1031 is the base 10 repunit (10 1031 ...
For example, 6 is highly composite because d(6)=4 and d(n)=1,2,2,3,2 for n=1,2,3,4,5 respectively. A related concept is that of a largely composite number , a positive integer that has at least as many divisors as all smaller positive integers.
The Miller–Rabin primality test and Solovay–Strassen primality test are more sophisticated variants, which detect all composites (once again, this means: for every composite number n, at least 3/4 (Miller–Rabin) or 1/2 (Solovay–Strassen) of numbers a are witnesses of compositeness of n). These are also compositeness tests.
These numbers are stored internally in a format equivalent to scientific notation, typically in binary but sometimes in decimal. Because floating-point numbers have limited precision, only a subset of real or rational numbers are exactly representable; other numbers can be represented only approximately.
A number that has the same number of digits as the number of digits in its prime factorization, including exponents but excluding exponents equal to 1. A046758 Extravagant numbers
In number theory, a superior highly composite number is a natural number which, ... 2 4 ⋅ 3 2 ⋅ 5 ⋅ 7 ⋅ 11 : 4,2,1,1,1 120 2 2 ⋅ 6 ⋅ 2310 : 10 720720: