64 (number)

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← 63 64 65 →
Cardinal sixty-four
Ordinal 64th
(sixty-fourth)
Factorization 26
Divisors 1, 2, 4, 8, 16, 32, 64
Greek numeral ΞΔ´
Roman numeral LXIV
Binary 10000002
Ternary 21013
Senary 1446
Octal 1008
Duodecimal 5412
Hexadecimal 4016

64 (sixty-four) is the natural number following 63 and preceding 65.

Contents

Mathematics

Sixty-four is the square of 8, the cube of 4, and the sixth power of 2. It is the seventeenth interprime, since it lies midway between the eighteenth and nineteenth prime numbers (61, 67). [1]

The aliquot sum of a power of two (2 n) is always one less than the power of two itself, therefore the aliquot sum of 64 is 63, within an aliquot sequence of two composite members (64, 63, 41, 1, 0) that are rooted in the aliquot tree of the thirteenth prime, 41. [2]

64 is:

Since it is possible to find sequences of 65 consecutive integers (intervals of length 64) such that each inner member shares a factor with either the first or the last member, 64 is the seventh Erdős–Woods number. [10]

In decimal, no integer added to the sum of its own digits yields 64; hence, 64 is the tenth self number. [11]

In four dimensions, there are 64 uniform polychora aside from two infinite families of duoprisms and antiprismatic prisms, and 64 Bravais lattices. [12]

In other fields

Science

64 is the atomic number of gadolinium, a lanthanide.

64 is the number of codons in the RNA codon table of the genetic code.

64 is the size in bits of certain data types in some computer programming languages, where a 64-bit integer can represent values up to 264 = 18,446,744,073,709,551,616.

Gaming

A chessboard has 64 squares. Chess Board.svg
A chessboard has 64 squares.

64 is the number of squares in a regular eight by eight chessboard.

64 is the maximum item stack size in Minecraft , where the number is called a 'stack'.

The 1996 Nintendo console is also called the Nintendo 64.

I Ching

The number of hexagrams in the I Ching (that is also the maximum number of strokes in any Chinese character).

Media

Song When I'm Sixty-Four by The Beatles

See also

Related Research Articles

70 (seventy) is the natural number following 69 and preceding 71.

90 (ninety) is the natural number following 89 and preceding 91.

34 (thirty-four) is the natural number following 33 and preceding 35.

46 (forty-six) is the natural number following 45 and preceding 47.

58 (fifty-eight) is the natural number following 57 and preceding 59.

63 (sixty-three) is the natural number following 62 and preceding 64.

92 (ninety-two) is the natural number following 91 and preceding 93

100 or one hundred is the natural number following 99 and preceding 101.

1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.

300 is the natural number following 299 and preceding 301.

2000 is a natural number following 1999 and preceding 2001.

3000 is the natural number following 2999 and preceding 3001. It is the smallest number requiring thirteen letters in English.

4000 is the natural number following 3999 and preceding 4001. It is a decagonal number.

135 is the natural number following 134 and preceding 136.

100,000 (one hundred thousand) is the natural number following 99,999 and preceding 100,001. In scientific notation, it is written as 105.

168 is the natural number following 167 and preceding 169.

1728 is the natural number following 1727 and preceding 1729. It is a dozen gross, or one great gross. It is also the number of cubic inches in a cubic foot.

240 is the natural number following 239 and preceding 241.

888 is the natural number following 887 and preceding 889.

262 is a natural number preceded by the number 261 and followed by 263. It has the prime factorization 2·131.

References

  1. ↑ Sloane, N. J. A. (ed.). "SequenceA024675(Average of two consecutive odd primes.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-11-06.
  2. ↑ Sloane, N. J. A., ed. (1975). "Aliquot sequences". The On-Line Encyclopedia of Integer Sequences . 29 (129). The OEIS Foundation: 101–107. Retrieved 2023-11-06.
  3. ↑ Sloane, N. J. A. (ed.). "SequenceA005179(Smallest number with exactly n divisors)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  4. ↑ Sloane, N. J. A. (ed.). "SequenceA030516(Numbers with 7 divisors. 6th powers of primes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  5. ↑ Sloane, N. J. A. (ed.). "SequenceA019279(Superperfect numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  6. ↑ Sloane, N. J. A. (ed.). "SequenceA002088(Sum of totient function: a(n) is Sum_{k equal to 1..n} phi(k), cf. A000010.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-11-06.
  7. ↑ Sloane, N. J. A. (ed.). "SequenceA006125(a(n) equal to 2^(n*(n-1)/2).)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-01-16.
  8. ↑ Sloane, N. J. A. (ed.). "SequenceA051624(12-gonal (or dodecagonal) numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  9. ↑ Sloane, N. J. A. (ed.). "SequenceA005448(Centered triangular numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  10. ↑ "Sloane's A059756 : Erdős-Woods numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  11. ↑ "Sloane's A003052 : Self numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  12. ↑ Brown, Harold; Bülow, Rolf; Neubüser, Joachim; Wondratschek, Hans; Zassenhaus, Hans (1978), Crystallographic groups of four-dimensional space, New York: Wiley-Interscience [John Wiley & Sons], ISBN   978-0-471-03095-9, MR   0484179
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