In
mathematics, a semiprime is a
natural number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country").
Numbers used for counting are called ''cardinal ...
that is the
product
Product may refer to:
Business
* Product (business), an item that serves as a solution to a specific consumer problem.
* Product (project management), a deliverable or set of deliverables that contribute to a business solution
Mathematics
* Produ ...
of exactly two
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 ...
s. The two primes in the product may equal each other, so the semiprimes include the
squares of prime numbers.
Because there are infinitely many prime numbers, there are also infinitely many semiprimes. Semiprimes are also called biprimes.
Examples and variations
The semiprimes less than 100 are:
Semiprimes that are not square numbers are called discrete, distinct, or squarefree semiprimes:
The semiprimes are the case
of the
-
almost primes, numbers with exactly
prime factors. However some sources use "semiprime" to refer to a larger set of numbers, the numbers with at most two prime factors (including unit (1), primes, and semiprimes). These are:
Formula for number of semiprimes
A semiprime counting formula was discovered by E. Noel and G. Panos in 2005. Let
denote the number of semiprimes less than or equal to n. Then