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
- Scientific notation
- 2.570 × 10^2
Roman numerals
C C L V I I
Binary
1 0 0 0 0 0 0 0 1
1 × 256 + 0 × 128 + 0 × 64 + 0 × 32 + 0 × 16 + 0 × 8 + 0 × 4 + 0 × 2 + 1 × 1 = 257
Octal
4 0 1
4 × 64 + 0 × 8 + 1 × 1 = 257
Hexadecimal
1 0 1
1 × 256 + 0 × 16 + 1 × 1 = 257
Read as powers of two: 256 + 1 = 257.
In historical numeral systems
Egyptian
2 coils of rope, 5 hobbles, 7 strokes
2 × 100 + 5 × 10 + 7 × 1 = 257. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.
Babylonian
4 vertical wedges (sixties place), 1 corner wedge + 7 vertical wedges (units place)
4 × 60 + 17 = 257. Places are separated by a space on the tablet, with the higher place written first.
Greek (Ionic)
sigma, then nu, then zeta, marked as a numeral
sigma-nu-zeta + keraia
sigma + nu + zeta written in descending order and added — the letters carry their values wherever they stand, so this is addition, not place value.
Hebrew numerals
resh, then nun, then zayin
resh-nun-zayin
resh (200) + nun (50) + zayin (7) = 257, written in descending order.
Maya
2 bars + 2 dots (upper, twenties place) over 3 bars + 2 dots (lower, units place)
12 × 20 + 17 = 257. Places stack vertically with the smallest at the bottom, so the upper group is worth twenty times the lower.
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
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: 15 July 2026