1135 is an ordinary natural number that can be discussed both as an integer with arithmetic properties and as a calendar year in the 12th century. As a numeral it sits between 1134 and 1136; as a year it marks a turning point in English medieval history. This article summarizes its mathematical character, historical significance, and other common contexts where the number appears.

Mathematical characteristics

Arithmetically, 1135 is an odd composite number. Its prime factorization is 5 × 227, so it is a semiprime (the product of exactly two primes). Its positive divisors are:

  • 1, 5, 227, 1135

Key number-theoretic values include:

  • Number of divisors (τ): 4
  • Sum of divisors (σ): 1368, so the sum of proper divisors is 233 (making 1135 a deficient number)
  • Euler's totient (φ): 904
  • Roman numeral: MCXXXV; hexadecimal: 0x46F; binary: 10001101111

Year AD 1135 (historical overview)

The year 1135 is most often cited for the death of King Henry I of England on 1 December. Henry's death precipitated a dynastic crisis because his designated heir, his daughter Empress Matilda, was challenged by her cousin Stephen of Blois, who quickly seized the English throne. The resulting period of civil war and instability in England and Normandy is commonly referred to as The Anarchy and lasted for many years, with wide-ranging political and social effects.

Context, uses, and occurrences

Beyond its mathematical identity and historical meaning as a year, 1135 appears routinely as an identifier: in addresses, product model numbers, catalogue entries, or file names. Numerically simple properties—such as ending with the digit 5—make it easy to recognize and to test for divisibility by 5. As with any four-digit number, its uses in dating and labeling are practical rather than intrinsically notable.

Distinctions and notable facts

Some concise distinctions: 1135 is not prime, not a square, not triangular, and not perfect. Its semiprime nature (5 × 227) places it in a common class of integers studied in basic factorization problems. Historically, its greatest notability derives from the events of AD 1135 in England, which had long-term consequences for medieval governance and succession law.

Overall, 1135 serves as a straightforward example in elementary number theory and as a shorthand reference to the turbulent year in early 12th-century English history.