1023 (number)
| ||||
|---|---|---|---|---|
| Cardinal | one thousand twenty-three | |||
| Ordinal | 1023rd (one thousand twenty-third) | |||
| Factorization | 3 × 11 × 31 | |||
| Divisors | 1, 3, 11, 31, 33, 93, 341, 1023 | |||
| Greek numeral | ,ΑΚΓ´ | |||
| Roman numeral | MXXIII | |||
| Binary | 11111111112 | |||
| Ternary | 11012203 | |||
| Quaternary | 333334 | |||
| Quinary | 130435 | |||
| Senary | 44236 | |||
| Octal | 17778 | |||
| Duodecimal | 71312 | |||
| Hexadecimal | 3FF16 | |||
| Vigesimal | 2B320 | |||
| Base 36 | SF36 | |||
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 [math]\displaystyle{ 2^{n}-1 }[/math].[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]
[math]\displaystyle{ (1, \mathbf {1023}, 28501, 145750, 246730, 179487, 63987, 11880, 1155, \mathbf {55}, 1) }[/math]
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]
1023 is the number of elements in the 9-simplex, as well as the number of uniform polytopes in the tenth-dimensional hypercubic family [math]\displaystyle{ \mathrm B_{10} }[/math], and the number of noncompact solutions in the family of paracompact honeycombs [math]\displaystyle{ \tilde T {9} }[/math] that shares symmetries with [math]\displaystyle{ \mathrm E_{10} }[/math].
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 [math]\displaystyle{ 2^{10}-1 }[/math], is the maximum number that a 10-bit ADC converter can return when measuring the highest voltage in range.
See also
References
- ↑ Sloane, N. J. A., ed. "Sequence A000225 (Mersenne numbers)". OEIS Foundation. https://oeis.org/A000225. Retrieved 2022-11-01.
- ↑ Sloane, N. J. A., ed. "Sequence A008277 (Triangle of Stirling numbers of the second kind, S2(n,k), n greater than or equal to 1, with 1 less than or equal to k less than or equal to n.)". OEIS Foundation. https://oeis.org/A008277. Retrieved 2023-12-09.
- ↑ Sloane, N. J. A., ed. "Sequence A034964 (Sums of five consecutive primes.)". OEIS Foundation. https://oeis.org/A034964. Retrieved 2022-11-01.
- ↑ Sloane, N. J. A., ed. "Sequence A133562 (Numbers which are the sum of the squares of seven consecutive primes.)". OEIS Foundation. https://oeis.org/A133562. Retrieved 2023-12-02.
- ↑ Sloane, N. J. A., ed. "Sequence A000162 (Number of 3-dimensional polyominoes (or polycubes) with n cells.)". OEIS Foundation. https://oeis.org/A000162. Retrieved 2022-11-01.
- ↑ Sloane, N. J. A., ed. "Sequence A008949 (Triangle read by rows of partial sums of binomial coefficients...also dimensions of Reed-Muller codes.)". OEIS Foundation. https://oeis.org/A008949. Retrieved 2022-11-01.
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