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
- Scientific notation
- 8.191 × 10^3
Roman numerals
Roman numerals as modelled here goes up to 3,999.
Binary
1 1 1 1 1 1 1 1 1 1 1 1 1
1 × 4,096 + 1 × 2,048 + 1 × 1,024 + 1 × 512 + 1 × 256 + 1 × 128 + 1 × 64 + 1 × 32 + 1 × 16 + 1 × 8 + 1 × 4 + 1 × 2 + 1 × 1 = 8,191
Octal
1 7 7 7 7
1 × 4,096 + 7 × 512 + 7 × 64 + 7 × 8 + 7 × 1 = 8,191
Hexadecimal
1 f f f
1 × 4,096 + f × 256 + f × 16 + f × 1 = 8,191
Read as powers of two: 4,096 + 2,048 + 1,024 + 512 + 256 + 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 8,191.
In historical numeral systems
Egyptian
8 lotuses, 1 coil of rope, 9 hobbles, 1 stroke
8 × 1,000 + 1 × 100 + 9 × 10 + 1 × 1 = 8,191. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.
Systems that simply cannot reach this value are left out. Where a script needs a font most readers do not have, the reading is given instead of the glyphs — see number systems for each system in full.
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: 15 July 2026