210 (number)

210 is the natural number following 209 and preceding 211.

In mathematics

210 is a composite number, an abundant number, and the product of the first four prime numbers (2, 3, 5, and 7), and thus a primorial. It is also 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 (following 190 and preceding 231), a pentagonal number (following 176 and preceding 247), and the second smallest to be both triangular and pentagonal (the third is 40755).

It is also a pentatope number, a pronic number, a Harshad number, and an untouchable number. 210 is also the first 71-gonal number, preceding 418.

See also: AD 210 or 210 BC.

211–219

Two hundred eleven 211 prime, primorial prime, sum of three consecutive primes (67 + 71 + 73), balanced prime, Chen prime, centered decagonal number, self number, also, SMTP status code for system status----Two hundred twelve 212 = 2²·53, totient sum for the first 26 integers, Zuckerman number. Also in degrees Fahrenheit, the boiling point of water at sea level.----Two hundred thirteen 213 = 3·71, Blum integer----Two hundred fourteen 214 = 2·107, Mertens function returns 0, nontotient, form DD 214 documents discharge from the U.S. Armed Forces, SMTP status code for help message
Number to which balance inquiry is sent (for subscribers of the Philippine telecommunications company Smart) "Sample request:" ?1515 "send to" 214
Title of one of the first hit songs of the popular Filipino band Rivermaya (released in 1994), which reached the Number One spot shortly after its release

----Two hundred fifteen 215 = 5·43. Form DD 215 is for corrections to form DD 214. Repdigit in base 6 (555).
The area code for a large portion of the Philadelphia Metropolitan Area----Two hundred sixteen 216 = 2³·3³ = 6³ = 3³ + 4³ + 5³, making it the smallest cube that is also the sum of three cubes; sum of a twin prime (107 + 109), untouchable number, Harshad number, Zuckerman number, also the number of colors in the Netscape Web-safe color palette; also ISO 216 is the ISO's standard for paper sizes 216 is the magic product for the smallest possible multiplicative magic square. [http://cboyer.club.fr/multimagie/English/Multiplicative.htm]

216 and 12,960,000 are Plato's numbers. [http://mathworld.wolfram.com/PlatosNumbers.html] ----Two hundred seventeen 217 = 7·31, Blum integer, centered hexagonal number----Two hundred eighteen 218 = 2·109, Mertens function(218) = 3 a record high that stands until 219, nontotient, noncototient

§ 218 is the section of the German StGB legal code that relates to abortion.

218 is the number of votes required in the US House of Representatives to achieve a majority. [http://news.bbc.co.uk/2/hi/americas/7652112.stm] ----Two hundred nineteen 219 = 3·73, Mertens function(219) = 4 a record high that stands until 221, 219 is a repdigit in base 8 (333).

There are 219 space groups in 3 dimensions, analogous to the 17 wallpaper groups in 2 dimensions. 11 of them have 2 forms each, with left-hand screw and right-hand screw (see screw axis), so from this perspective there are 230 space groups.

References