Definitions for prime number
prime num·ber

Princeton's WordNetRate this definition:0.0 / 0 votes

1. prime numbernoun

   an integer that has no integral factors but itself and 1

WiktionaryRate this definition:0.0 / 0 votes

1. prime numbernoun

   Any natural number greater than 1 divisible only by itself and 1.

WikipediaRate this definition:0.0 / 0 votes

1. 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.

ChatGPTRate this definition:0.0 / 0 votes

1. prime number

   A prime number is a natural number greater than 1 that has no positive divisors other than 1 itself and the number. In other words, a prime number is a number that cannot be formed by multiplying two smaller natural numbers. Examples of prime numbers include 2, 3, 5, 7, 11, 13, 17, and so on.

WikidataRate this definition:5.0 / 1 vote

1. Prime number

   A prime number 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 only 1 and 5 evenly divide it, 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 copies of 1 in any factorization, e.g., 3, 1 × 3, 1 × 1 × 3, etc. are all valid factorizations of 3. The property of being prime is called primality. A simple but slow method of verifying the primality of a given number n is known as trial division. It consists of testing whether n is a multiple of any integer between 2 and . Algorithms that are much more efficient than trial division have been devised to test the primality of large numbers. Particularly fast methods are available for numbers of special forms, such as Mersenne numbers. As of February 2013, the largest known prime number has 17,425,170 decimal digits.

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How to pronounce prime number?

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How to say prime number in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of prime number in Chaldean Numerology is: 8

2. Pythagorean Numerology

   The numerical value of prime number in Pythagorean Numerology is: 8

Examples of prime number in a Sentence

1. Anonymous:

   Enter any 11-digit prime number to continue...

2. John Blasik:

   It was mentioned on CNN that the new prime number discovered recently is four times bigger then the previous record.

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=prime number
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Prime_Number
3. ^ Wikipedia
   https://en.wikipedia.org/wiki/Prime_Number
4. ^ ChatGPT
   https://chat.openai.com
5. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=prime number