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.
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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\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.
 
  
 
==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

  • $9$ 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

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