1023 (number) explained

Number:	1023
Divisor:	1, 3, 11, 31, 33, 93, 341, 1023

1023 (one thousand [and] twenty-three) is the natural number following 1022 and preceding 1024.

Mathematics

1023 is the tenth non-trivial Mersenne number of the form

2 ^{n} -1 .^[1] In binary, it is also the tenth repdigit 1111111111₂ as all Mersenne numbers in decimal are repdigits in binary.

As a Mersenne number, it is the first non-unitary member of the eleventh row (left to right) in the triangle of Stirling partition numbers^[2]

$$(1,\; \backslash mathbf,\; 28501,\; 145750,\; 246730,\; 179487,\; 63987,\; 11880,\; 1155,\; \backslash mathbf,\; 1)$$

that appears opposite a triangular number (successively in each row), in its case 55.

It is equal to the sum of five consecutive prime numbers: 193 + 197 + 199 + 211 + 223.^[3]

It is equal to the sum of the squares of the first seven consecutive odd prime numbers: 3² + 5² + 7² + 11² + 13² + 17² + 19².^[4]

It is the number of three-dimensional polycubes with seven cells.^[5]

B _{10} , and the number of noncompact solutions in the family of paracompact honeycombs \tilde T _{9} that shares symmetries with E _{10} .

In other fields

Computing

Floating-point units in computers often run a IEEE 754 64-bit, floating-point excess-1023 format in 11-bit binary. In this format, also called binary64, the exponent of a floating-point number (e.g. 1.009001 E1031) appears as an unsigned binary integer from 0 to 2047, where subtracting 1023 from it gives the actual signed value.

1023 is the number of dimensions or length of messages of an error-correcting Reed-Muller code made of 64 block codes.^[6]

Technology

The Global Positioning System (GPS) works on a ten-digit binary counter that runs for 1023 weeks, at which point an integer overflow causes its internal value to roll over to zero again.

1023 being

2 ^{10} -1 , is the maximum number that a 10-bit ADC converter can return when measuring the highest voltage in range.

See also

1024 (number)

Notes and References

1. 2022-11-01 .
2. 2023-12-09 .
3. 2022-11-01 .
4. 2023-12-02 .
5. 2022-11-01 .
6. 2022-11-01 .