3511 (three thousand, five hundred and eleven) is the
natural number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country").
Numbers used for counting are called ''Cardinal n ...
following 3510 and preceding 3512.
3511 is a
prime number
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 ...
, and is also an
emirp
An emirp (''prime'' spelled backwards) is a prime number that results in a different prime when its decimal digits are reversed. This definition excludes the related palindromic primes. The term ''reversible prime'' is used to mean the same as ...
: a different prime when its
digits are reversed.
3511 is a
Wieferich prime
In number theory, a Wieferich prime is a prime number ''p'' such that ''p''2 divides , therefore connecting these primes with Fermat's little theorem, which states that every odd prime ''p'' divides . Wieferich primes were first described by Ar ...
,
found to be so by
N. G. W. H. Beeger
Nicolaas George Wijnand Henri Beeger (1884, in Utrecht – 1965, in Amsterdam) was a Dutch mathematician. His 1916 doctorate was on Dirichlet series. He worked for most of his life as a teacher, working on mathematics papers in his spare evenin ...
in 1922 and the largest known
[ – the only other being 1093. If any other Wieferich primes exist, they must be greater than 6.7.]centered decagonal number
A centered decagonal number is a centered figurate number that represents a decagon with a dot in the center and all other dots surrounding the center dot in successive decagonal layers. The centered decagonal number for ''n'' is given by the ...
.
References
Integers
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