280 (number)

280 (two hundred [and] eighty) is the natural number after 279 and before 281.

In mathematics

The denominator of the eighth harmonic number, 280 is an octagonal number.

There are 280 plane trees with ten nodes. As a consequence of this, 18 people around a round table can shake hands with each other in non-crossing ways, in 280 different ways (this includes rotations).

280 is a base 10 Harshad number.

In geography

• List of highways numbered 280

See also the year 280.

281 to 289

281

Two hundred [and] eighty-one 281 prime, twin prime with 283, Sophie Germain prime, sum of the first fourteen primes, sum of seven consecutive primes (29 + 31 + 37 + 41 + 43 + 47 + 53), Chen prime, Eisenstein prime with no imaginary part, centered decagonal number

282

Two hundred [and] eighty-two 282 = 2·3·47, sphenic number

283

Two hundred [and] eighty-three 283 prime, twin prime with 281, strictly non-palindromic number

284

Two hundred [and] eighty-four 284= 2·2·71, amicable number with 220; nontotient. 284 degrees Celsius is the flash point of paper.

285

Two hundred [and] eighty-five 285 = 3·5·19, sphenic number, square pyramidal number, Harshad number, also in Star Trek, the total number of Rules of Acquisition, repdigit in base 7 (555).

286

Two hundred [and] eighty-six 286 = 2·11·13, sphenic number, tetrahedral number, nontotient, also shorthand for the Intel 80286 microprocessor chip

287

Two hundred [and] eighty-seven 287 = 7·41, sum of three consecutive primes (89 + 97 + 101), sum of five consecutive primes (47 + 53 + 59 + 61 + 67), sum of nine consecutive primes (17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47), Kynea number, pentagonal number, also shorthand for the Intel math coprocessor to the 80286

288

Two hundred [and] eighty-eight 288 = 2⁵·3², is a pentagonal pyramidal number, is 4 superfactorial since 288 = 1!·2!·3!·4!, is an untouchable number, a Harshad number in base 10, a self number, is sum of the sequence of integers 1..4 to the second tetration since 288 = 1 + 4 + 27 + 256 = 1¹ + 2² + 3³ + 4⁴, the number of labelled pointed rooted trees (vertebrates) with up to 4 nodes, the number of maximal directed Pseudoforests on up to 4 vertices, the number of Endofunctions for all sets with <=4 points, and is two dozen sets of a dozen, thus being two gross, often told as a pun in maths classes.

289

Two hundred [and] eighty-nine 289 = 17², centered octagonal number, Friedman number since (8 + 9)^2 = 289.