Semiprime

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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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