1023 (number)

Last updated
← 1022 1023 1024 →
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
Senary 44236
Octal 17778
Duodecimal 71312
Hexadecimal 3FF16

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

Contents

Mathematics

1023 is the tenth non-trivial 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)

Related Research Articles

2 (two) is a number, numeral and digit. It is the natural number following 1 and preceding 3. It is the smallest and only even prime number. Because it forms the basis of a duality, it has religious and spiritual significance in many cultures.

19 (nineteen) is the natural number following 18 and preceding 20. It is a prime number.

23 (twenty-three) is the natural number following 22 and preceding 24.

32 (thirty-two) is the natural number following 31 and preceding 33.

31 (thirty-one) is the natural number following 30 and preceding 32. It is a prime number.

61 (sixty-one) is the natural number following 60 and preceding 62.

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.

360 is the natural number following 359 and preceding 361.

400 is the natural number following 399 and preceding 401.

127 is the natural number following 126 and preceding 128. It is also a prime number.

500 is the natural number following 499 and preceding 501.

700 is the natural number following 699 and preceding 701.

600 is the natural number following 599 and preceding 601.

2000 is a natural number following 1999 and preceding 2001.

<span class="mw-page-title-main">1,000,000</span> Natural number

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<span class="mw-page-title-main">1,000,000,000</span> Natural number

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10,000,000 is the natural number following 9,999,999 and preceding 10,000,001.

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References

  1. ↑ Sloane, N. J. A. (ed.). "SequenceA000225(Mersenne numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2022-11-01.
  2. ↑ Sloane, N. J. A. (ed.). "SequenceA008277(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.). "SequenceA034964(Sums of five consecutive primes.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2022-11-01.
  4. ↑ Sloane, N. J. A. (ed.). "SequenceA133562(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.). "SequenceA000162(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.). "SequenceA008949(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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