prime number - определение. Что такое prime number
Diclib.com
Словарь ChatGPT
Введите слово или словосочетание на любом языке 👆
Язык:

Перевод и анализ слов искусственным интеллектом ChatGPT

На этой странице Вы можете получить подробный анализ слова или словосочетания, произведенный с помощью лучшей на сегодняшний день технологии искусственного интеллекта:

  • как употребляется слово
  • частота употребления
  • используется оно чаще в устной или письменной речи
  • варианты перевода слова
  • примеры употребления (несколько фраз с переводом)
  • этимология

Что (кто) такое prime number - определение

POSITIVE INTEGER WITH EXACTLY TWO DIVISORS, 1 AND ITSELF
Primes; Prime numbers; Prime factor; Primality; Prime Numbers; Prime factors; Odd prime; 1 no longer prime; Prime divisor; Prime numbers in nature; Even primes; Prime Number; Infinity of primes; Prime-Numbers; Euclidean prime number theorem; Table Of Primes List; Prime; Primalities; Prime-number; Uncompound number; Odd prime number; Ω(n); Primality of 1; A000040; 1 is not a prime number; Prime (number); Primenumber; Primality of one; Infinity of the primes; Draft:The first mathematical of the prime numbers; Draft:Integer X prime matrix
  • The [[Gaussian prime]]s with norm less than 500
  • The small gear in this piece of farm equipment has 13 teeth, a prime number, and the middle gear has 21, relatively prime to 13
  • alt=Construction of a regular pentagon using straightedge and compass
  • relative error]] of <math>\tfrac{n}{\log n}</math> and the logarithmic integral <math>\operatorname{Li}(n)</math> as approximations to the [[prime-counting function]]. Both relative errors decrease to zero as <math>n</math> grows, but the convergence to zero is much more rapid for the logarithmic integral.
  • alt=Demonstration, with Cuisenaire rods, that 7 is prime, because none of 2, 3, 4, 5, or 6 divide it evenly
  • alt=Groups of two to twelve dots, showing that the composite numbers of dots (4, 6, 8, 9, 10, and 12) can be arranged into rectangles but prime numbers cannot
  • alt=The Rhind Mathematical Papyrus
  • alt=Plot of the absolute values of the zeta function
  • alt=Animation of the sieve of Eratosthenes
  • The connected sum of two prime knots
  • alt=The Ulam spiral

prime number         
(prime numbers)
In mathematics, a prime number is a whole number greater than 1 that cannot be divided exactly by any whole number except itself and the number 1, for example 17.
N-COUNT
Prime number         
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number.
prime         
I. a.
1.
First, original, primitive, primal, primeval, primordial, pristine, aboriginal.
2.
Highest, chief, principal.
3.
Early, blooming.
4.
First-rate, capital, excellent.
II. n.
1.
Beginning, opening, first part, earliest stage, dawn, morning.
2.
Youth, spring of life, early days.
3.
Perfection, flower, greatest beauty, health, or strength, best days, cream.

Википедия

Prime number

A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order.

The property of being prime is called primality. A simple but slow method of checking the primality of a given number n {\displaystyle n} , called trial division, tests whether n {\displaystyle n} is a multiple of any integer between 2 and n {\displaystyle {\sqrt {n}}} . Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error, and the AKS primality test, which always produces the correct answer in polynomial time but is too slow to be practical. Particularly fast methods are available for numbers of special forms, such as Mersenne numbers. As of December 2018 the largest known prime number is a Mersenne prime with 24,862,048 decimal digits.

There are infinitely many primes, as demonstrated by Euclid around 300 BC. No known simple formula separates prime numbers from composite numbers. However, the distribution of primes within the natural numbers in the large can be statistically modelled. The first result in that direction is the prime number theorem, proven at the end of the 19th century, which says that the probability of a randomly chosen large number being prime is inversely proportional to its number of digits, that is, to its logarithm.

Several historical questions regarding prime numbers are still unsolved. These include Goldbach's conjecture, that every even integer greater than 2 can be expressed as the sum of two primes, and the twin prime conjecture, that there are infinitely many pairs of primes having just one even number between them. Such questions spurred the development of various branches of number theory, focusing on analytic or algebraic aspects of numbers. Primes are used in several routines in information technology, such as public-key cryptography, which relies on the difficulty of factoring large numbers into their prime factors. In abstract algebra, objects that behave in a generalized way like prime numbers include prime elements and prime ideals.

Примеры употребления для prime number
1. Other oddities include variations on pi and products of prime number multiplication.
2. Mathematicians at UCLA have discovered a 13 million–digit prime number, a long–sought milestone that makes them eligible for a $100,000 prize.
3. LOS ANGELES –– Mathematicians at UCLA have discovered a 13–million–digit prime number, a long–sought milestone that makes them eligible for a $100,000 prize.
4. The foundation supports individual rights on the Internet and set up the prime number prize to promote cooperative computing using the Web.
5. However, mathematicians had great difficulty in finding a pattern to prime number distribution until, in the 1'th century, GFB Riemann worked out an elaborate equation which suggested the existence of such a pattern.