A centered heptagonal number is a
centered figurate number that represents a
heptagon
In geometry, a heptagon or septagon is a seven-sided polygon or 7-gon.
The heptagon is sometimes referred to as the septagon, using ''Wikt:septa-, septa-'' (an elision of ''Wikt:septua-, septua-''), a Latin-derived numerical prefix, rather than ...
with a dot in the center and all other dots surrounding the center dot in successive heptagonal layers. The centered heptagonal number for ''n'' is given by the formula
:
.
The first few centered heptagonal numbers are
1,
8,
22,
43,
71,
106,
148,
197, 253, 316, 386, 463, 547, 638, 736, 841, 953
Centered heptagonal prime
A centered heptagonal prime is a centered heptagonal number that is
prime
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...
. The first few centered heptagonal primes are
:43, 71, 197, 463, 547, 953, 1471, 1933, 2647, 2843, 3697, ...
The centered heptagonal
twin prime
A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair or In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin prime' ...
numbers are
:43, 71, 197, 463, 1933, 5741, 8233, 9283, 11173, 14561, 34651, ...
See also
*Regular
heptagonal number.
References
{{Classes of natural numbers
Figurate numbers