Number analysis
1,000
1,000 is a composite even number that factors as 2^3 × 5^3.
1,000 is a composite even number that factors as 2^3 × 5^3.
The number itself
- Value
- 1,000
- Digits
- 4
- Digit sum
- 1
- Reversed
- 1
- Palindrome
- No
1 + 0 + 0 + 0
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reverses to 1.
Parity and primality
- Parity
- Even
- Prime
- No
- Prime factorisation
- 2^3 × 5^3
- Squarefree
- No
- Powerful
- Yes
- Möbius μ(n)
- 0
- Nearest primes
- 997 ← → 1,009
Divisible by 2.
Composite — it factors as 2^3 × 5^3.
2 distinct prime factors, 6 with multiplicity.
At least one prime appears squared.
Every prime factor appears at least squared.
Zero, because a squared prime divides n.
A gap of 12 between them.
Divisors
- Sum of divisors σ(n)
- 2,340
- Aliquot sum
- 1,340
- Classification
- Abundant
1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1,000
The proper divisors — everything except n itself.
Its proper divisors overshoot by 340.
How many integers from 1 to n share no factor with n.
Sums and additive structure
- Sum of two squares
- Yes
- Sum of three squares
- Yes
- Sum of four squares
- Yes
- Sum of two cubes
- 0³ + 10³
- Goldbach pair
- 3 + 997
10² + 30² = 1,000 · 18² + 26² = 1,000
Legendre's three-square theorem allows it.
Lagrange's four-square theorem: every non-negative integer is, without exception.
The smallest pair of primes summing to n. Goldbach’s conjecture says one always exists; it remains unproven.
Shapes and sequences
- Perfect cube
- Yes — 10³
Digit curiosities
- Happy number
- Yes
- Harshad number
- Yes
- Collatz trajectory
- 111 steps to 1
Repeatedly summing the squares of its digits reaches 1.
Divisible by its digit sum 1 — 1,000 ÷ 1 = 1,000.
Peaks at 9,232 along the way.
Written other ways
- Binary
- 1111101000
- Octal
- 1750
- Hexadecimal
- 3E8
- Base 36
- RS
- In words
- one thousand
- Scientific notation
- 1.000 × 10^3
Is 1,000 a prime number?
Composite — it factors as 2^3 × 5^3.
Nearby numbers
Other numeral systems
Beyond the bases and Roman numerals above, these notations write 1,000 their own way.
- Greek (alphabetic)
- ͵Α
- Tamil
- ௲
- Thai
- ๑๐๐๐
References
Further reading: Wikipedia · MathWorld · Wikidata
Notations, naming and the links above come from Wikidata, whose structured data is dedicated to the public domain under CC0-1.0. Retrieved 2026-10-07.