257
257 is a Fermat prime, and one of only five known.
- Odd
- Prime
Where 257 fits
Why 257 is special
Fermat conjectured that every number of this form is prime. The first five — 3, 5, 17, 257 and 65,537 — are, and every one tested since has been composite. They survive in geometry rather than in number theory: Gauss showed these are exactly the odd primes for which a regular polygon of that many sides can be constructed with compass and straightedge.
257 is part of
Factors & digit properties
- Divisors (2)
- 1, 257
- Prime factorisation
- 257
- Digit sum
- 14
- Digital root
- 5
Representations
- Decimal
- 257
- Binary
- 100000001
- Octal
- 401
- Hexadecimal
- 101
- Roman numeral
- CCLVII
- Scientific notation
- 2.570 × 10^2
Other mathematical patterns
- Deficient number
Related numbers & connections
Rwanda and Burundi share a border, a language family and a colonial history, and both are among the most densely populated countries in Africa.
View 250 →Two of the five known Fermat primes. 65,537 is the largest, and is the public exponent used by most RSA encryption in the world because its bit pattern makes the arithmetic cheap.
View 65537 →Geography
+257 reaches Burundi, which combines high population density with very low urbanisation. Almost everyone lives rurally, which is an unusual pairing.
DocumentedGeographyGeography: Burundi
Mathematics
Gauss proved that a regular polygon is constructible with compass and straightedge exactly when its number of sides is a power of two times distinct Fermat primes — which is why the 17-sided polygon can be drawn and the 7-sided one cannot. That theorem is the reason these five numbers matter outside arithmetic. Fermat believed every number of his form was prime; Euler found a counterexample in 1732, and every case tested since has been composite.
DocumentedMathematics
Common questions
Is 257 a prime number?
Yes, 257 is prime — it has exactly two positive divisors: 1 and itself.
What are the factors of 257?
The factors of 257 are 1, 257.
What is 257 in Roman numerals?
257 in Roman numerals is CCLVII.
About this page's data
Mathematical facts:computed directly from the number's value — nothing to source or verify externally.
Contextual records: 2 reviewer-confirmed records, sourced and reviewed before publication.
Last reviewed: 3 August 2026