1024 (number)

1024 is the

1024 is a

1024 is the smallest number with exactly 11 divisors (but there are smaller numbers with more than 11 divisors; e.g., 60 has 12 divisors) (sequence A005179 in the OEIS).

Enumeration of groups

The number of

This count is more than 99% of all the isomorphism classes of groups of order less than 2000.[7]

Approximation to 1000

The neat coincidence that 2¹⁰ is nearly equal to 10³ provides the basis of a technique of estimating larger powers of 2 in decimal notation. Using 2^10a+b ≈ 2^b10^3a(or 2^a≈2^{a mod 10}10^floor(a/10) if "a" stands for the whole power) is fairly accurate for exponents up to about 100. For exponents up to 300, 3a continues to be a good estimate of the number of digits.

For example, 2⁵³ ≈ 8×10¹⁵. The actual value is closer to 9×10¹⁵.

In the case of larger exponents, the relationship becomes increasingly inaccurate, with errors exceeding an order of magnitude for a ≥ 97. For example:

${\displaystyle {\begin{aligned}{\frac {2^{1000}}{10^{300}}}&=\exp \left(\ln \left({\frac {2^{1000}}{10^{300}}}\right)\right)\\&=\exp \left(\ln \left(2^{1000}\right)-\ln \left(10^{300}\right)\right)\\&\approx \exp \left(693.147-690.776\right)\\&\approx \exp \left(2.372\right)\\&\approx 10.72\end{aligned}}}$

In measuring

Special use in computers

In binary notation, 1024 is represented as 10000000000, making it a simple round number occurring frequently in computer applications.

1024 is the maximum number of computer

In the Rich Text Format (RTF), language code 1024 indicates the text is not in any language and should be skipped over when proofing. Most used languages codes in RTF are integers slightly over 1024.

1024×

1024 is the lowest non-system and non-reserved port number in TCP/IP networking. Ports above this number can usually be opened for listening by non-superusers.

See also

• Powers of 1024

References