← 1022 1023 1024 →
Cardinalone thousand twenty-three
Ordinal1023rd
(one thousand twenty-third)
Factorization3 × 11 × 31
Divisors1, 3, 11, 31, 33, 93, 341, 1023
Greek numeral,ΑΚΓ´
Roman numeralMXXIII
Binary11111111112
Ternary11012203
Senary44236
Octal17778
Duodecimal71312
Hexadecimal3FF16

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

Mathematics

1023 is the tenth non-zero Mersenne number of the form .[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]

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 , and the number of noncompact solutions in the family of paracompact honeycombs that shares symmetries with .

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

See also

1024 (number)

References

  1. ↑ Sloane, N. J. A. (ed.). "Sequence A000225 (Mersenne numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-11-01.
  2. ↑ 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.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-12-09.
  3. ↑ Sloane, N. J. A. (ed.). "Sequence A034964 (Sums of five consecutive primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-11-01.
  4. ↑ Sloane, N. J. A. (ed.). "Sequence A133562 (Numbers which are the sum of the squares of seven consecutive primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-12-02.
  5. ↑ Sloane, N. J. A. (ed.). "Sequence A000162 (Number of 3-dimensional polyominoes (or polycubes) with n cells.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-11-01.
  6. ↑ Sloane, N. J. A. (ed.). "Sequence A008949 (Triangle read by rows of partial sums of binomial coefficients...also dimensions of Reed-Muller codes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-11-01.
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