Number analysis
8,191
8,191 is a prime number — divisible only by 1 and itself.
8,191 is a prime number — divisible only by 1 and itself.
The number itself
- Value
- 8,191
- Digits
- 4
- Digit sum
- 19
- Reversed
- 1,918
- Palindrome
- No
8 + 1 + 9 + 1
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reverses to 1,918.
Parity and primality
- Parity
- Odd
- Prime
- Yes
- Prime factorisation
- 8191
- Squarefree
- Yes
- Möbius μ(n)
- -1
- Mersenne prime
- 2^13 − 1
- Nearest primes
- 8,179 ← → 8,209
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 30 between them.
Divisors
- Sum of divisors σ(n)
- 8,192
- Aliquot sum
- 1
- Classification
- Deficient
- Euler totient φ(n)
- 8,190
1, 8,191
The proper divisors — everything except n itself.
Its proper divisors fall short by 8,190.
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
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.
Shapes and sequences
- Figurate shapes
- None
Not triangular, square, pentagonal, hexagonal, cubic, Fibonacci, Lucas, Catalan, factorial or a power of two.
Digit curiosities
- Happy number
- No
- Harshad number
- No
- Collatz trajectory
- 158 steps to 1
Summing the squares of its digits falls into the 4 → 16 → 37 → … → 4 cycle.
Not divisible by its digit sum 19.
Peaks at 6,810,136 along the way.
Written other ways
- Binary
- 1111111111111
- Octal
- 17777
- Hexadecimal
- 1FFF
- Base 36
- 6BJ
- In words
- eight thousand one hundred and ninety-one
- Scientific notation
- 8.191 × 10^3
Standard Roman numerals only run from 1 to 3,999.
Is 8,191 a prime number?
Yes. 8,191 has no divisors other than 1 and itself.