Difference between revisions of "Semiprime"

(Put more information about semiprimes.)
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==Examples==
 
==Examples==
*<math>9</math> is an example of a semiprime as it is the product of two threes. <math>3*3=9</math>.
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*<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>.
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*<math>17</math>, as it is only a prime number.
 
*<math>17</math>, as it is only a prime number.
 
*<math>12</math>, not a semiprime because it can obtained by <math>3*4</math> or <math>2*6</math>.
 
*<math>12</math>, not a semiprime because it can obtained by <math>3*4</math> or <math>2*6</math>.
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== Basic Properties==
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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.
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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 19:10, 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

  • $9$ 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 \[n=2ab+a+b\quad 0<a,b<n a,b,n\in\mathbb{N}\], 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

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