213 (two hundred
ndthirteen) is the number following
212
Year 212 ( CCXII) was a leap year starting on Wednesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Asper and Camilius (or, less frequently, year 965 '' Ab urbe condit ...
and preceding
214.
In mathematics
213 and the other permutations of its digits are the only three-digit number whose
digit sum
In mathematics, the digit sum of a natural number in a given number base is the sum of all its digits. For example, the digit sum of the decimal number 9045 would be 9 + 0 + 4 + 5 = 18.
Definition
Let n be a natural number. We define the digit ...
s and digit products are equal. It is a member of the quickly-growing Levine sequence, constructed from a triangle of numbers in which each row counts the copies of each value in the row below it.
As the product of the two distinct prime numbers 3 and 71, it is a
semiprime
In mathematics, a semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other, so the semiprimes include the squares of prime numbers.
Because there are infinitely many prime ...
, the first of a triple of three consecutive semiprimes 213, 214, and 215. Its square, 213
2 = 45369, is one of only 15 known squares that can be represented as a sum of distinct
factorials
In mathematics, the factorial of a non-negative denoted is the product of all positive integers less than or equal The factorial also equals the product of n with the next smaller factorial:
\begin
n! &= n \times (n-1) \times (n-2) \t ...
.
See also
*
213 (disambiguation)
References
Integers
{{Num-stub
ca:Nombre 210#Nombres del 211 al 219