Difference between revisions of "Semiprime"
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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>. | + | *<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== | ||
+ | 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
is an example of a semiprime as it is the product of two threes.
.
is also an example as it is obtained by
.
Other examples include: ,
,
,
,
, and
.
Examples of non-semiprimes
, as it is only a prime number.
, not a semiprime because it can obtained by
or
.
Basic Properties
Via the Sieve of Sundaram formulation of: being composite any time
, as
, we can show that if and only if
are both not composite producing then
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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