Difference between revisions of "Semiprime"

Revision as of 15:37, 25 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.

@@ Line 11: / Line 11: @@
 == 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\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.
+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.

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Difference between revisions of "Semiprime"

Revision as of 15:37, 25 February 2020

Contents

Examples

Examples of non-semiprimes

Basic Properties

See Also