Difference between revisions of "Semiprime"

(Basic Properties)
(Examples)
 
Line 2: Line 2:
  
 
==Examples==
 
==Examples==
*<math>9</math> is an example of a semiprime as it is the product of two threes. <math>3\*3=9</math>.
+
*<math>9</math> is an example of a semiprime as it is the product of two threes. <math>3*3=9</math>.
 
*<math>10</math> is also an example as it is obtained by <math>5*2</math>.
 
*<math>10</math> is also an example as it is obtained by <math>5*2</math>.
 
Other examples include: <math>25</math>, <math>15</math>, <math>39</math>, <math>221</math>, <math>437</math>, and <math>1537</math>.
 
Other examples include: <math>25</math>, <math>15</math>, <math>39</math>, <math>221</math>, <math>437</math>, and <math>1537</math>.

Latest revision as of 19:05, 28 May 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

  • $9$ is an example of a semiprime as it is the product of two threes. $3*3=9$.
  • $10$ is also an example as it is obtained by $5*2$.

Other examples include: $25$, $15$, $39$, $221$, $437$, and $1537$.

Examples of non-semiprimes

  • $17$, as it is only a prime number.
  • $12$, not a semiprime because it can obtained by $3*4$ or $2*6$.

Basic Properties

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