210 (two hundred ndten) 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

209 Year 209 ( CCIX) was a common year starting on Sunday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Commodus and Lollianus (or, less frequently, year 962 '' Ab urbe cond ...

and preceding 211.

In mathematics

210 is a

composite number A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime, ...

, an

abundant number In number theory, an abundant number or excessive number is a number for which the sum of its proper divisors is greater than the number. The integer 12 is the first abundant number. Its proper divisors are 1, 2, 3, 4 and 6 for a total of 16. The ...

, Harshad number, and the product of the first four

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 ...

s ( 2, 3, 5, and 7), and thus a

primorial In mathematics, and more particularly in number theory, primorial, denoted by "#", is a function from natural numbers to natural numbers similar to the factorial function, but rather than successively multiplying positive integers, the function ...

. It is also the least common multiple of these four prime numbers. It is the sum of eight consecutive prime numbers (13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 = 210).Wells, D. (1987). ''The Penguin Dictionary of Curious and Interesting Numbers'' (p. 143). London: Penguin Group. It is a

triangular number A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots in ...

(following 190 and preceding

231 Year 231 ( CCXXXI) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Claudius and Sallustus (or, less frequently, year 984 '' Ab urbe ...

), a

pentagonal number A pentagonal number is a figurate number that extends the concept of triangular and square numbers to the pentagon, but, unlike the first two, the patterns involved in the construction of pentagonal numbers are not rotationally symmetrical. The ...

(following

176 Year 176 ( CLXXVI) was a leap year starting on Sunday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Proculus and Aper (or, less frequently, year 929 '' Ab urbe condita'') ...

and preceding 247), and the second smallest to be both triangular and pentagonal (the third is 40755). It is also an

idoneal number In mathematics, Leonhard Euler, Euler's idoneal numbers (also called suitable numbers or convenient numbers) are the positive integers ''D'' such that any integer expressible in only one way as ''x''2 ± ''Dy''2 (where ''x''2 is relativel ...

, a

pentatope number A pentatope number is a number in the fifth cell of any row of Pascal's triangle starting with the 5-term row , either from left to right or from right to left. The first few numbers of this kind are: : 1, 5, 15, 35, 70, 126, 210, 330, 495 ...

, a

pronic number A pronic number is a number that is the product of two consecutive integers, that is, a number of the form n(n+1).. The study of these numbers dates back to Aristotle. They are also called oblong numbers, heteromecic numbers,. or rectangular number ...

, and an

untouchable number An untouchable number is a positive integer that cannot be expressed as the sum of all the proper divisors of any positive integer (including the untouchable number itself). That is, these numbers are not in the image of the aliquot sum function. ...

. 210 is also the third 71-gonal number, preceding

418 __NOTOC__ Year 418 ( CDXVIII) was a common year starting on Tuesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Honorius and Theodosius (or, less frequently, year 11 ...

. It is the first primorial number greater than 2 which is not adjacent to 2 primes (211 is prime, but 209 is not). It is the largest number ''n'' such that all primes between ''n''/2 and ''n'' yield a representation as a sum of two primes.

References

{{Integers, 2 Integers

In mathematics

See also

References