210 (number)

Source: Wikipedia, the free encyclopedia.
← 209 210 211 →
10, 14, 15, 21, 30, 35, 42, 70, 105, 210
Greek numeralΣΙ´
Roman numeralCCX
Binary110100102
Ternary212103
Senary5506
Octal3228
Duodecimal15612
HexadecimalD216

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

Mathematics

210 is an

7), and thus a primorial,[2] where it is the least common multiple of these four prime numbers. 210 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 sum of eight consecutive prime numbers, between 13 and the thirteenth prime number: 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 = 210.[3]

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).[3]

It is also an

418.[3]

210 is index n = 7 in the number of ways to pair up {1, ..., 2n} so that the sum of each pair is prime; i.e., in {1, ..., 14}.[4][5]

It is the largest number n where the number of distinct representations of n as the sum of two primes is at most the number of primes in the interval [n/2 , n − 2].[6]

Integers between 211 and 219

211

Main article: 211 (number)

212

Main article: 212 (number)

213

Main article: 213 (number)

214

Main article: 214 (number)

215

Main article: 215 (number)

216

Main article: 216 (number)

217

Main article: 217 (number)

218

Main article: 218 (number)

219

Main article: 219 (number)

See also

  • 210 BC
  • AD 210
  • North American telephone area code
    area code 210

References

  1. ^ Sloane, N. J. A. (ed.). "Sequence A005101 (Abundant numbers (sum of divisors of m exceeds 2m).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-02-10.
  2. ^ Sloane, N. J. A. (ed.). "Sequence A002110 (Primorial numbers (first definition): product of first n primes. Sometimes written prime(n)#.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-02-10.
  3. ^ a b c Wells, D. (1987). The Penguin Dictionary of Curious and Interesting Numbers (p. 143). London: Penguin Group.
  4. ^ Sloane, N. J. A. (ed.). "Sequence A000341 (Number of ways to pair up {1..2n} so sum of each pair is prime.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-02-10.
  5. Zbl 1010.11007
    .
  6. doi:10.1090/S0025-5718-1993-1202609-9
    .
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