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210 (number)

FieldValue
number210
divisor[1](1-number), [2](2-number), [3](3-number), [5](5-number), [6](6-number), [7](7-number), [10](10-number), [14](14-number), [15](15-number), [21](21-number), [30](30-number), [35](35-number), [42](42-number), [70](70-number), [105](105-number), 210

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

Mathematics

210 is an abundant number, and Harshad number. It is the product of the first four prime numbers (2, 3, 5, and 7), and thus a primorial, 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:

It is the 20th 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 first is 1; the third is 40755).

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

210 is index in the number of ways to pair up so that the sum of each pair is prime; i.e., in .

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 .

References

References

  1. {{Cite OEIS. A005101. Abundant numbers (sum of divisors of m exceeds 2m).
  2. {{Cite OEIS. A002110. Primorial numbers (first definition): product of first n primes. Sometimes written prime(n)#.
  3. Wells, D. (1987). ''The Penguin Dictionary of Curious and Interesting Numbers'' (p. 143). London: Penguin Group.
  4. "A000217 - OEIS".
  5. {{Cite OEIS. A000326. pentagonal number
  6. {{Cite OEIS. A000341. Number of ways to pair up {1..2n} so sum of each pair is prime.
  7. (1998). "Some Problems of Combinatorial Number Theory Related to Bertrand's Postulate". [[David R. Cheriton School of Computer Science]].
  8. (1993). "An upper bound in Goldbach's problem". Mathematics of Computation.
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