1001

1001 is a natural number that follows 1000 and precedes 1002. It is a four-digit number in the decimal system. It also serves as a year designation: the year 1001 in the Julian calendar was the second year of the 11th century.

The number has notable mathematical properties, particularly regarding its factors. Culturally, it is connected to the title of the stories 'Alf Layla wa Layla' (One Thousand and One Nights), which gave 1001 a literary meaning extending beyond arithmetic.

Mathematical properties

1001 is a composite number (not prime): it equals 7 × 11 × 13. Because all three factors are distinct primes, it is known as a sphenic number. For this reason, 7, 11, and 13 are commonly taught together as the 'factors of 1001'.

A distinctive divisibility test is based on 1001: when a number is multiplied by 1001, the result repeats the number twice in sequence (for example: 123 × 1001 = 123123). This makes it possible to check whether a number is divisible by 7, 11, or 13 by applying a three-digit grouping method.

1001 is also a palindrome—it reads the same forwards and backwards. It is also a binomial number: 1001 equals the number of ways to choose four items from a set of fourteen (C(14,4)), and thus appears in Pascal's triangle.

The year 1001

As a year, 1001 marks the early 11th century in the Julian calendar, which was in use across much of Europe at that time. Other calendars—such as the Islamic calendar—reckon different years at the same period, so conversion of dates requires care.

Culture

The title 'One Thousand and One Nights' gave 1001 a meaning of 'very many' or 'countless', distinct from the strict numerical value. This usage has spread to many languages and appears in book titles, films, and commercial names.