1137 is an integer that follows 1136 and precedes 1138. In arithmetic it is an odd, positive whole number with a small set of divisors and several simple representations in common numeral systems. It appears both as a plain mathematical value and as a designation for the calendar year 1137 AD, which features in medieval European history.

Mathematical properties

As a number, 1137 is composite and factors as 3 × 379, where 379 is a prime. Because it is the product of two distinct odd primes each congruent to 3 modulo 4, 1137 qualifies as a Blum integer, a special type of semiprime important in certain cryptographic and number‑theoretic contexts.

Arithmetic invariants and simple representations include:

  • Divisors: 1, 3, 379, 1137.
  • Euler totient: φ(1137) = (3−1)(379−1) = 756.
  • Sum of divisors: σ(1137) = 1 + 3 + 379 + 1137 = 1520 (proper divisors sum = 383).
  • Binary: 10001110001; hexadecimal: 0x471; Roman numeral: MCXXXVII.

History and the year 1137 (AD)

When used as a year number, 1137 denotes the 12th century AD. In European medieval history it is remembered for dynastic transitions and marriages that shaped later politics. Notably, King Louis VI of France died in 1137 and was succeeded by his son Louis VII. In the same year, Eleanor of Aquitaine, one of the most influential noblewomen of the Middle Ages, married Louis VII and thereby became Queen of France; this union had significant political and cultural consequences in subsequent decades.

Beyond Europe, the year belongs to a period of broad social and political change across Asia, the Islamic world and Africa, but specific events vary by region. As with any single year in the distant past, surviving records are uneven and focus more on political and ecclesiastical affairs.

Usage and notable distinctions

Outside pure mathematics and chronology, the sequence "1137" can serve as an identifier in catalogues, model numbers or archival references; such uses are incidental and context-dependent. In number theory, its classification as a semiprime and as a Blum integer gives it modest relevance to studies of factorization, quadratic residues and cryptographic constructions that rely on products of particular primes.

Overall, 1137 is a straightforward composite number with clear arithmetic features and a place in medieval chronology; its interest lies mainly in those two, distinct roles.