# Difference between revisions of "Semiprime"

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== Basic Properties== | == Basic Properties== | ||

− | Via the Sieve of Sundaram formulation of: <cmath>2n+1=</cmath> being composite any time <cmath>n=2ab+a+b\quad 0<a,b<n a,b,n\in\mathbb{N}</cmath>, as <math>2n+1=4ab+2a+2b+1=(2a+1)(2b+1)</math>, we can show that if and only if <math>a,b</math> are both not composite producing then <math>2n+1</math> is a semiprime. | + | Via the Sieve of Sundaram formulation of: <cmath>2n+1=</cmath> being composite any time <cmath>n=2ab+a+b\quad 0<a,b<n\quad a,b,n\in\mathbb{N}</cmath>, as <math>2n+1=4ab+2a+2b+1=(2a+1)(2b+1)</math>, we can show that if and only if <math>a,b</math> are both not composite producing then <math>2n+1</math> is a semiprime. |

Odd semiprimes, are able to be expressed as a difference of squares, like all other numbers that are products of numbers of same parity. | Odd semiprimes, are able to be expressed as a difference of squares, like all other numbers that are products of numbers of same parity. | ||

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==See Also== | ==See Also== |

## Revision as of 19:11, 24 February 2020

In mathematics, a **semiprime** is a number that is the product of two not necessarily distinct primes. These integers are important in many contexts, including cryptography.

## Examples

- is an example of a semiprime as it is the product of two threes. .
- is also an example as it is obtained by .

Other examples include: , , , , , and .

## Examples of non-semiprimes

- , as it is only a prime number.
- , not a semiprime because it can obtained by or .

## Basic Properties

Via the Sieve of Sundaram formulation of: being composite any time , as , we can show that if and only if are both not composite producing then is a semiprime.

Odd semiprimes, are able to be expressed as a difference of squares, like all other numbers that are products of numbers of same parity.

## See Also

*This article is a stub. Help us out by expanding it.*