Number analysis
8,128
The fourth perfect number, known to the Greeks.
The fourth perfect number, known to the Greeks.
The number itself
- Value
- 8,128
- Digits
- 4
- Digit sum
- 19
- Reversed
- 8,218
- Palindrome
- No
8 + 1 + 2 + 8
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reverses to 8,218.
Parity and primality
- Parity
- Even
- Prime
- No
- Prime factorisation
- 2^6 × 127
- Squarefree
- No
- Möbius μ(n)
- 0
- Nearest primes
- 8,123 ← → 8,147
Divisible by 2.
Composite — it factors as 2^6 × 127.
2 distinct prime factors, 7 with multiplicity.
At least one prime appears squared.
Zero, because a squared prime divides n.
A gap of 24 between them.
Divisors
- Sum of divisors σ(n)
- 16,256
- Aliquot sum
- 8,128
- Classification
- Perfect
- Euler totient φ(n)
- 4,032
1, 2, 4, 8, 16, 32, 64, 127, 254, 508, 1,016, 2,032, 4,064, 8,128
The proper divisors — everything except n itself.
Its proper divisors sum to exactly itself.
How many integers from 1 to n share no factor with n.
Sums and additive structure
- Sum of two squares
- No
- Sum of three squares
- No
- Sum of four squares
- Yes
- Goldbach pair
- 5 + 8,123
A prime congruent to 3 mod 4 divides it an odd number of times, which rules it out.
Excluded by Legendre: it has the form 4^a(8b + 7).
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
- Triangular number
- Yes — the 127th
- Hexagonal number
- Yes — the 64th
Digit curiosities
- Happy number
- Yes
- Harshad number
- No
- Collatz trajectory
- 52 steps to 1
Repeatedly summing the squares of its digits reaches 1.
Not divisible by its digit sum 19.
Peaks at 8,128 along the way.
Written other ways
- Binary
- 1111111000000
- Octal
- 17700
- Hexadecimal
- 1FC0
- Base 36
- 69S
- In words
- eight thousand one hundred and twenty-eight
- Scientific notation
- 8.128 × 10^3
Standard Roman numerals only run from 1 to 3,999.
Is 8,128 a prime number?
Composite — it factors as 2^6 × 127.
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.