1289

1289 is a positive integer with several notable mathematical properties. It is a prime number, meaning its only positive divisors are 1 and 1289, and it is odd. Because 1289 ≡ 1 (mod 4), it can be expressed as the sum of two squares; one representation is 8^2 + 35^2.

In different numeral systems, 1289 has distinct representations. In Roman numerals it is MCCLXXXIX. In binary it is 10100001001, and in hexadecimal it is 0x509.

As a year, 1289 falls in the late 13th century and, in the Julian calendar, was a common year (not a leap year). The year is part of historical chronologies that document the medieval world, including political, religious and cultural developments across various regions. In mathematics, 1289 is sometimes cited for its sum-of-squares representation and its status as a prime number, illustrating properties studied in number theory such as primes congruent to 1 modulo 4 and representations by Gaussian integers.

Summary: 1289 is a prime, odd integer with representations as 8^2 + 35^2, MCCLXXXIX in Roman numerals, 10100001001 in binary, and 0x509 in hexadecimal. As a year, it marks a point in the late 13th century within the Julian calendar.