Search results
Results From The WOW.Com Content Network
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. This fact is called the fundamental theorem of arithmetic. [5] [6] [7] [8]
The primes form an infinite sequence 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, ... Composite number : A positive integer that can be factored into a product of smaller positive integers. Every integer greater than one is either prime or composite.
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) .
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ... The prime numbers p n , with n ≥ 1 . A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers.
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.
In number theory, a Smith number is a composite number for which, in a given number base, the sum of its digits is equal to the sum of the digits in its prime factorization in the same base. In the case of numbers that are not square-free , the factorization is written without exponents, writing the repeated factor as many times as needed.
In number theory, a superior highly composite number is a natural number which, in a particular rigorous sense, ... 2 4 ⋅ 3 2 ⋅ 5 ⋅ 7 ⋅ 11 ⋅ 13 : 4,2,1,1,1 ...
So if it is unknown whether a number n is prime or composite, we can pick a random number a, calculate the Jacobi symbol ( a / n ) and compare it with Euler's formula; if they differ modulo n, then n is composite; if they have the same residue modulo n for many different values of a, then n is "probably prime".