1259

1259 is a natural number that comes after 1258 and before 1260. It is a prime number, meaning it has no positive divisors other than 1 and itself. It is odd, and its digits sum to 17, giving a digital root of 8. In modular arithmetic, 1259 ≡ 3 (mod 4); as a consequence, it cannot be expressed as a sum of two squares of integers.

In common numeral systems, 1259 is represented as 10011101011 in binary, 2353 in octal, and 0x4EB in hexadecimal. In Roman numerals it is written as MCCLIX. As a prime number, 1259 has exactly two positive divisors: 1 and 1259. It is not a triangular number, not a square or cube, and lies between the Fibonacci numbers 987 and 1597, so it is not itself a Fibonacci number. It is also not a safe prime, since (1259 − 1) / 2 equals 629, which factors as 17 × 37.

As a year, 1259 CE falls in the 13th century, a period marked by ongoing medieval political realignments and Crusade-era dynamics in Europe and the broader Mediterranean world. Specific events in that year vary by region and source. In number theory, 1259 is cited primarily as an example of a small prime congruent to 3 modulo 4.