260 (number)

← 259 260 261 →
Cardinal two hundred sixty
Ordinal 260th
(two hundred and sixtieth)
Factorization 22× 5 × 13
Roman numeral CCLX
Binary 1000001002
Ternary 1001223
Quaternary 100104
Quinary 20205
Senary 11126
Octal 4048
Duodecimal 19812
Hexadecimal 10416
Vigesimal D020
Base 36 7836

260 (two hundred [and] sixty) is the magic constant of the n×n normal magic square and n-queens problem for n = 8, the size of an actual chess board.

260 is also the magic constant of the Franklin magic square devised by Benjamin Franklin.

52 61 4 13 20 29 36 45
14 3 62 51 46 35 30 19
53 60 5 12 21 28 37 44
11 6 59 54 43 38 27 22
55 58 7 10 23 26 39 42
9 8 57 56 41 40 25 24
50 63 2 15 18 31 34 47
16 1 64 49 48 33 32 17

The minor diagonal gives 260, and in addition a number of combinations of two half diagonals of four numbers from a corner to the center give 260.

260 may also refer to the years AD 260 and 260 BC.

261–269

261 = 32·29, lucky number, nonagonal number, Harshad number, unique period in base 2, number of possible unfolded tesseract patterns

262 = 2·131, meandric number, open meandric number, untouchable number, happy number, palindrome number, semiprime

263 has its own article. 263 is a prime, safe prime, happy number, sum of five consecutive primes (43 + 47 + 53 + 59 + 61), balanced prime, Chen prime, Eisenstein prime with no imaginary part, strictly non-palindromic number, Bernoulli irregular prime, Euler irregular prime, Gaussian prime, full reptend prime, Solinas prime, Ramanujan prime.

264 = 23·3·11, Harshad number. If you take the sum of all 2-digit numbers you can make from 264, you get 264: 24 + 42 + 26 + 62 + 46 + 64 = 264. 132 and 396 share this property.[1]

264 equals the sum of the squares of the digits of its own square in base 15. This property is shared with 1, 159, 284, 306 and 387.

265 = 5·53, semiprime, lucky number, Padovan number, number of derangements of 6 elements, centered square number, Smith number, subfactorial 6.

266 = 2·7·19, sphenic number, Harshad number, nontotient, noncototient, self number, repdigit in base 11 (222). 266 is also the index of the largest proper subgroups of the sporadic group known as the Janko group J1.

267 = 3·89, semiprime, the number of groups of order 64.[2]

268 = 22·67, noncototient, untouchable number

269 has its own article. 269 is a prime, twin prime with 271, sum of three consecutive primes (83 + 89 + 97), Chen prime, Eisenstein prime with no imaginary part, highly cototient number, strictly non-palindromic number, full reptend prime

References

  1. ↑ Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 138
  2. ↑ Number of groups of order n
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