Number analysis
10,000
10,000 is a composite even number that factors as 2^4 × 5^4.
10,000 is a composite even number that factors as 2^4 × 5^4.
The number itself
- Value
- 10,000
- Digits
- 5
- Digit sum
- 1
- Reversed
- 1
- Palindrome
- No
1 + 0 + 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
- 2^4 × 5^4
- Squarefree
- No
- Powerful
- Yes
- Möbius μ(n)
- 0
- Nearest primes
- 9,973 ← → 10,007
Divisible by 2.
Composite — it factors as 2^4 × 5^4.
2 distinct prime factors, 8 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 34 between them.
Divisors
- Sum of divisors σ(n)
- 24,211
- Aliquot sum
- 14,211
- Classification
- Abundant
- Euler totient φ(n)
- 4,000
1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 625, 1,000, … (5 more)
The proper divisors — everything except n itself.
Its proper divisors overshoot by 4,211.
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
- Goldbach pair
- 59 + 9,941
0² + 100² = 10,000 · 28² + 96² = 10,000 · 60² + 80² = 10,000
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
- Square number
- Yes — the 100th
Digit curiosities
- Happy number
- Yes
- Harshad number
- Yes
- Collatz trajectory
- 29 steps to 1
Repeatedly summing the squares of its digits reaches 1.
Divisible by its digit sum 1 — 10,000 ÷ 1 = 10,000.
Peaks at 10,000 along the way.
Written other ways
- Binary
- 10011100010000
- Octal
- 23420
- Hexadecimal
- 2710
- Base 36
- 7PS
- In words
- ten thousand
- Scientific notation
- 1.0000 × 10^4
Standard Roman numerals only run from 1 to 3,999.
Is 10,000 a prime number?
Composite — it factors as 2^4 × 5^4.
Nearby numbers
References
Further reading: Wikipedia · 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.