Number analysis
3
3 is a prime number — divisible only by 1 and itself.
3 is a prime number — divisible only by 1 and itself.
The number itself
- Value
- 3
- Digits
- 1
- Digit sum
- 3
- Reversed
- 3
- Palindrome
- Yes
3
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reads the same in both directions.
Parity and primality
- Parity
- Odd
- Prime
- Yes
- Squarefree
- Yes
- Möbius μ(n)
- -1
- Mersenne prime
- 2^2 − 1
- Fermat prime
- 2^1 + 1
- Sophie Germain prime
- Yes — 2n+1 = 7 is also prime
- Twin prime
- Yes — paired with 5
- Nearest primes
- 2 ← → 5
Leaves remainder 1 on division by 2.
Divisible only by 1 and itself.
1 distinct prime factor, 1 with multiplicity.
No prime divides it twice.
(−1) to the power of 1 distinct prime factors.
A gap of 3 between them.
Divisors
- Aliquot sum
- 1
- Classification
- Deficient
1, 3
The proper divisors — everything except n itself.
Its proper divisors fall short by 2.
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
- Yes
- Sum of four squares
- Yes
A prime congruent to 3 mod 4 divides it an odd number of times, which rules it out.
Legendre's three-square theorem allows it.
Lagrange's four-square theorem: every non-negative integer is, without exception.
Shapes and sequences
- Triangular number
- Yes — the 2nd
- Fibonacci number
- Yes — index 4
- Lucas number
- Yes — index 2
Digit curiosities
- Happy number
- No
- Armstrong number
- Yes, trivially
- Harshad number
- Yes
- Collatz trajectory
- 7 steps to 1
Summing the squares of its digits falls into the 4 → 16 → 37 → … → 4 cycle.
Every single-digit number equals itself raised to the first power, so all ten qualify trivially.
Divisible by its digit sum 3 — 3 ÷ 3 = 1.
Peaks at 16 along the way.
Written other ways
- Binary
- 11
- Octal
- 3
- Base 36
- 3
- Roman numerals
- III
- In words
- three
- Scientific notation
- 3 × 10^0
Is 3 a prime number?
Yes. 3 has no divisors other than 1 and itself.
Nearby numbers
Other numeral systems
Beyond the bases and Roman numerals above, these notations write 3 their own way.
- Greek (alphabetic)
- Γʹ
- Babylonian cuneiform
- 𒐈
- Tamil
- ௩
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.