Definition

1. Noun:
   • A whole number greater than 1 that cannot be formed by multiplying two smaller whole numbers: A prime number is a positive integer greater than 1 whose only divisors are 1 and itself. It has exactly two distinct positive divisors.

Usage

• The term "prime number" is used in mathematics, specifically in number theory.
• It is a countable noun (e.g., "a prime number," "the prime numbers," "three prime numbers").
• It is used to classify integers based on their divisibility properties.

Examples

• Noun:
  • 2, 3, 5, 7, and 11 are all prime numbers.
  • The number 15 is not a prime number because it can be divided by 3 and 5.
  • Mathematicians have studied prime numbers for centuries.

Advanced Usage

• "twin primes": A pair of prime numbers that differ by 2 (e.g., 3 and 5, 11 and 13).
  • The conjecture about twin primes is a famous unsolved problem in mathematics.
• "prime factorization": Expressing a number as a product of its prime factors.
  • The prime factorization of 12 is 2 x 2 x 3.

Variants and Related Words

• Prime (adjective): Of first importance; excellent quality. In mathematics, having the properties of a prime number (e.g., "a prime factor").
• Primeness (noun): The state or quality of being prime.
• Composite number (noun): A positive integer greater than 1 that is not prime (i.e., it has more than two divisors).

Synonyms

• Prime (when used as a noun in context, e.g., "Find all primes less than 20.").

Related Phrases and Concepts

• "relatively prime" or "coprime": Two numbers whose greatest common divisor is 1. They do not necessarily need to be prime numbers themselves.
  • The numbers 8 and 9 are relatively prime.
• "prime gap": The difference between successive prime numbers.
  • The prime gap between 7 and 11 is 4.

Noun

1. an integer that has no integral factors but itself and 1