1003 (number)

← 1002 1003 1004 →
Cardinalone thousand three
Ordinal1003rd
(one thousand third)
Factorization17 × 59
Divisors1, 17, 59, 1003
Greek numeral,ΑΓ´
Roman numeralMIII, miii
Binary11111010112
Ternary11010113
Senary43516
Octal17538
Duodecimal6B712
Hexadecimal3EB16

1003 (one thousand [and] three) is the natural number following 1002 and preceding 1004.

In mathematics

1003 is an odd composite number. It is also a happy number, the smallest 4-digit brilliant number and a Lucas 8-step number. 1003 is the 33rd term representing the vertex number of a square spiral whose first two edge lengths are the legs of the [3, 4, 5] primitive Pythagorean triple.

The number of times the digit 5 appears in the first 104 digits of Catalan's constant is 1003. The number of symmetric polynomial functions of degree 4 of a symmetric matrix of indefinitely large size under joint row and column permutations is also 1003. Also, 1003 is the number of fusenes that possess 22 hexagons and C3h symmetry containing 329 carbon atoms.

The term "100310 + 10039 + 10038 + 10037 + 10036 + 10035 + 10034 + 10033 + 10032 + 1003 + 1" is prime

Prime factorization

The prime factorization of 1003 is:

1003 = 17 × 59

This means that the divisors of 1003 are 1, 17, 59 and 1003.

Since the prime factorization of 1003 is the product of two distinct prime numbers, 1003 is a semiprime. It is also a square-free number, since no square divides it.

1003 is the smallest 4-digit brilliant number whose prime factorizations are concatenated in some order, is also brilliant, in other words, 5917 = 61 × 97.

See also

References

  1. 1 2 "Number 1003". Number World. Retrieved 2026-10-30.
  2. 1 2 Honaker, Jr., G. L.; McLean, Reginald. "1003". Prime Curios!. PrimePages. Retrieved 2026-10-30.
  3. ↑ Noe, Tony D.; Post, Jonathan Vos (2005). "Primes in Fibonacci n-step and Lucas n-step Sequences". Journal of Integer Sequences. 8 (05.4.4): 3. Retrieved 2026-10-30.
  4. ↑ Sloane, N. J. A. (ed.). "Sequence A195020 (Vertex number of a square spiral in which the length of the first two edges are the legs of the primitive Pythagorean triple [3, 4, 5]. The edges of the spiral have length A195019.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2026-10-30.
  5. ↑ Weisstein, Eric W. "Catalan's Constant Digits". MathWorld. Wolfram Research, Inc. Retrieved 2026-10-29.
  6. ↑ Sloane, N. J. A. (ed.). "Sequence A007717 (Number of symmetric polynomial functions of degree n of a symmetric matrix (of indefinitely large size) under joint row and column permutations. Also number of multigraphs with n edges (allowing loops) on an infinite set of nodes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2026-10-30.
  7. ↑ Sloane, N. J. A. (ed.). "Sequence A123285 (Number of fusenes with 22 hexagons, C_(3h) symmetry and containing 3n carbon atoms.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2026-10-30.
  8. ↑ Brinkmann, Gunnar; Caporossi, Gilles; Hansen, Pierre (2003-05-01). "A Survey and New Results on Computer Enumeration of Polyhex and Fusene Hydrocarbons". Journal of Chemical Information and Computer Sciences. 43 (3): 842–851. doi:10.1021/ci025526c. ISSN 0095-2338.
  9. ↑ Sloane, N. J. A. (ed.). "Sequence A162862 (Numbers n such that n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1 is prime.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2026-10-30.
  10. ↑ Crisan, Dragos; Erban, Radek. "On the counting function of semiprimes". arXiv:2006.16491 [math.NT].
  11. ↑ Grabowski, Adam (2013-06-01). "On Square-Free Numbers". Formalized Mathematics. 21 (2): 153–162. doi:10.2478/forma-2013-0017. ISSN 1898-9934.