The term 585 can denote the integer that follows 584 and precedes 586, or it can be used to identify the calendar years 585 BC and AD 585. As a number it exhibits several elementary arithmetical features that make it notable in basic number theory and recreational mathematics. As a year, 585 BC is traditionally remembered for a famous solar eclipse reported by ancient historians; AD 585 falls in the late antique/early medieval period within the framework of the Julian calendar.

Mathematical properties

Arithmetic factorization and divisor structure are often the first characteristics listed for a positive integer. The prime factorization of 585 is 32 · 5 · 13. From that factorization follow a small set of standard facts:

  • Number of positive divisors: 12.
  • Complete set of positive divisors: 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585.
  • Sum of all divisors: 1092; sum of proper divisors: 507, which is less than 585, so 585 is a deficient number.
  • 585 is divisible by 9 and by 5; in Roman numerals it is written DLXXXV.

Beyond factors, 585 has a few representational curiosities. In base ten it is palindromic (reads the same forward and backward). Its binary representation is 1001001001, which is also palindromic in that base. These symmetric patterns make 585 a common example in discussions of palindromic numbers.

Year 585 BC

The year 585 BC (using the proleptic Gregorian/Julian reckoning) is often cited in classical sources for an astronomical event: an eclipse of the Sun that, according to later historians, occurred while forces of two Anatolian kingdoms were in battle and brought a halt to the fighting. Ancient authors attribute the prediction of that eclipse to the pre-Socratic philosopher Thales of Miletus; this story is part of broader discussions about early Greek natural philosophy and the beginnings of scientific explanation in the Western tradition.

AD 585 and historical context

AD 585 occurred in the 6th century, a period characterized by transformations across Eurasia — movements of peoples in Europe, continuation of the Byzantine Empire, and the Sasanian Empire in Persia. Specific political and local developments of the year vary by region and source, but AD 585 sits within the era sometimes called the early Middle Ages in European history and late antiquity more generally.

Notable distinctions and uses

  • As a palindromic integer, 585 is frequently used in puzzles and demonstrations about base-dependent symmetry.
  • Its factor pattern (32 · 5 · 13) gives it a moderate number of divisors for a three-prime factorization, making it a simple example in elementary divisor-counting problems.
  • Historically, the eclipse associated with 585 BC plays a role in synchronizing ancient chronologies and in discussions of how astronomical events were recorded and interpreted in antiquity.

Whether encountered as an object of arithmetic curiosity or as a label for historical years, 585 connects straightforward numerical structure with moments that have been highlighted in historical traditions. Both aspects — the number's divisibility and palindromic representations, and the remembered eclipse in the 6th century BC — are the chief points of interest for readers approaching the entry from mathematical or historical perspectives.