210 (number)

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← 209 210 211 →
Cardinal two hundred ten
Ordinal 210th
(two hundred tenth)
Factorization 2 × 3 × 5 × 7
Divisors 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
Greek numeral ΣΙ´
Roman numeral CCX
Binary 110100102
Ternary 212103
Quaternary 31024
Quinary 13205
Senary 5506
Octal 3228
Duodecimal 15612
Hexadecimal D216
Vigesimal AA20
Base 36 5U36

210 (two hundred [and] ten) is the natural number following 209 and preceding 211.

In mathematics[edit]

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 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).[1]

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).[1]

It is also a idoneal number, a pentatope number, a pronic number, a Harshad number, and an untouchable number. 210 is also the first 71-gonal number, preceding 418.[1] 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.[2]

See also[edit]

References[edit]

  1. ^ a b c Wells, D. (1987). The Penguin Dictionary of Curious and Interesting Numbers (p. 143). London: Penguin Group.
  2. ^ Deshouillers, Jean-Marc; Granville, Andrew; Narkiewicz, Władysław; Pomerance, Carl (1993). "An upper bound in Goldbach's problem". Mathematics of Computation. 61 (203): 209–213. doi:10.1090/S0025-5718-1993-1202609-9Freely accessible.