Prime number

Demonstration, with Cuisenaire rods, that the number 7 is prime, being divisible only by 1 and 7

The number 12 is not a prime, as 12 items can be placed into 3 equal-size columns of 4 each (among other ways). 11 items cannot be all placed into several equal-size columns of more than 1 item each without some extra items leftover (a remainder). Therefore, the number 11 is a prime.

A chart depicting π(n) (blue), n / ln (n) (green) and Li(n) (red)

A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example, 5 is prime because 1 and 5 are its only positive integer factors, whereas 6 is composite because it has the divisors 2 and 3 in addition to 1 and 6. The fundamental theorem of arithmetic establishes the central role of primes in number theory: any integer greater than 1 can be expressed as a product of primes that is unique up to ordering. The uniqueness in this theorem requires excluding 1 as a prime because one can include arbitrarily many instances of 1 in any factorization, e.g., 3, 1 · 3, 1 · 1 · 3, etc. are all valid factorizations of 3.

单词	Primalities
释义	Primalities 英语例句库 Based on some basic theorems in theory of numbers this program takes advantage of probabilistic algorithm to test a large number for primality. 基于初等数论中的一些基本定理,本程序利用概率算法,快速判定一个大数是否为素数。英语百科 Prime number A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example, 5 is prime because 1 and 5 are its only positive integer factors, whereas 6 is composite because it has the divisors 2 and 3 in addition to 1 and 6. The fundamental theorem of arithmetic establishes the central role of primes in number theory: any integer greater than 1 can be expressed as a product of primes that is unique up to ordering. The uniqueness in this theorem requires excluding 1 as a prime because one can include arbitrarily many instances of 1 in any factorization, e.g., 3, 1 · 3, 1 · 1 · 3, etc. are all valid factorizations of 3.
随便看	esplanade的意思 esplanner的意思 esplees的意思 Esplegares的意思 espleit的意思 espleite的意思 E.splendens Bojer ex Hook.的意思 E.splendens Nakai ex F.Maekawa的意思 esplendor的意思 ESPLR的意思 Espluga Calva的意思 ESPN的意思 ESPN.com的意思 espnet的意思 ESPNews的意思 ESPN, Inc.的意思 espnoic的意思 ESPN的意思 ESPO的意思 espohageal epithelium的意思 Espoir的意思 Espoir的意思 ESPOL的意思 Espolla的意思 esponja的意思

Primalities

Prime number