131,071
131,071 is 2¹⁷ − 1, the sixth Mersenne prime.
- Odd
- Prime
Where 131,071 fits
Why 131,071 is special
Mersenne primes require the exponent itself to be prime, which 17 is — but that is necessary rather than sufficient, and most prime exponents produce composites. 2¹¹ − 1 is 2,047, which factors as 23 × 89, and that failure is what made the pattern interesting rather than obvious.
131,071 is part of
Factors & digit properties
- Divisors (2)
- 1, 131071
- Prime factorisation
- 131071
- Digit sum
- 13
- Digital root
- 4
Representations
- Decimal
- 131071
- Scientific notation
- 1.311 × 10^5
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 1 1 1
1 × 65,536 + 1 × 32,768 + 1 × 16,384 + 1 × 8,192 + 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 = 131,071
Octal
3 7 7 7 7 7
3 × 32,768 + 7 × 4,096 + 7 × 512 + 7 × 64 + 7 × 8 + 7 × 1 = 131,071
Hexadecimal
1 f f f f
1 × 65,536 + f × 4,096 + f × 256 + f × 16 + f × 1 = 131,071
Read as powers of two: 65,536 + 32,768 + 16,384 + 8,192 + 4,096 + 2,048 + 1,024 + 512 + 256 + 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 131,071.
In historical numeral systems
Egyptian
1 tadpole, 3 fingers, 1 lotus, 7 hobbles, 1 stroke
1 × 100,000 + 3 × 10,000 + 1 × 1,000 + 7 × 10 + 1 × 1 = 131,071. 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
- Mersenne prime
Common questions
Is 131,071 a prime number?
Yes, 131,071 is prime — it has exactly two positive divisors: 1 and itself.
What are the factors of 131,071?
The factors of 131,071 are 1, 131071.
About this page's data
Mathematical facts:computed directly from the number's value — nothing to source or verify externally.