8191
8,191 is a Mersenne prime — 2 to the 13th, minus one.
- Odd
- Prime
Where 8191 fits
Why 8191 is special
Mersenne primes are the form used to hold the record for the largest known prime for most of the modern era, because a fast test exists for that shape specifically and not for numbers in general. 8,191 was known by the fifteenth century.
8191 is part of
Factors & digit properties
- Divisors (2)
- 1, 8191
- Prime factorisation
- 8191
- Digit sum
- 19
- Digital root
- 1
Representations
- Decimal
- 8191
- Binary
- 1111111111111
- Octal
- 17777
- Hexadecimal
- 1fff
- Scientific notation
- 8.191 × 10^3
Other mathematical patterns
- Deficient number
- Lucky number (mathematical sieve)
- Mersenne prime
Mathematics
8,191 is 2^13 − 1, a Mersenne prime. Numbers of this form have held the largest-known-prime record for most of the modern era, not because they are more likely to be prime but because a fast test exists for that shape and not for numbers in general.
DocumentedMathematics
Common questions
Is 8191 a prime number?
Yes, 8191 is prime — it has exactly two positive divisors: 1 and itself.
What are the factors of 8191?
The factors of 8191 are 1, 8191.
About this page's data
Mathematical facts:computed directly from the number's value — nothing to source or verify externally.
Contextual records: 1 reviewer-confirmed record, sourced and reviewed before publication.
Last reviewed: 3 August 2026