1001 is the

natural number In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''Cardinal n ...

following 1000 and followed by

1002 Year 1002 (MII) was a common year starting on Thursday (link will display the full calendar) of the Julian calendar. Events By place Europe * January 23 – Emperor Otto III dies, at the age of 22, of smallpox at Castle of Pater ...

In mathematics

One thousand and one is a

sphenic number In number theory, a sphenic number (from grc, σφήνα, 'wedge') is a positive integer that is the product of three distinct prime numbers. Because there are infinitely many prime numbers, there are also infinitely many sphenic numbers. Definit ...

, a

pentagonal number A pentagonal number is a figurate number that extends the concept of triangular and square numbers to the pentagon, but, unlike the first two, the patterns involved in the construction of pentagonal numbers are not rotationally symmetrical. The ...

, a

pentatope number A pentatope number is a number in the fifth cell of any row of Pascal's triangle starting with the 5-term row , either from left to right or from right to left. The first few numbers of this kind are: : 1, 5, 15, 35, 70, 126, 210, 330, 4 ...

and the first four-digit

palindromic number A palindromic number (also known as a numeral palindrome or a numeric palindrome) is a number (such as 16461) that remains the same when its digits are reversed. In other words, it has reflectional symmetry across a vertical axis. The term ''palin ...

. Scheherazade numbers always have 1001 as a factor.

Divisibility by 7, 11 and 13

Two properties of 1001 are the basis of a divisibility test for 7, 11 and 13. The method is along the same lines as the divisibility rule for 11 using the property 10 ≡ -1 (mod 11). The two properties of 1001 are 1001 = 7 × 11 × 13 in prime factors 10³ ≡ -1 (mod 1001) The method simultaneously tests for divisibility by any of the factors of 1001. First, the digits of the number being tested are grouped in blocks of three. The odd numbered groups are summed. The sum of the even numbered groups is then subtracted from the sum of the odd numbered groups. The test number is divisible by 7, 11 or 13

iff In logic and related fields such as mathematics and philosophy, "if and only if" (shortened as "iff") is a biconditional logical connective between statements, where either both statements are true or both are false. The connective is bicon ...

the result of the summation is divisible by 7, 11 or 13 respectively. Example: Number under test, ''N'' = 22 872 563 219 Sum of odd groups, ''S''_o = 219 + 872 = 1091 Sum of even groups, ''S''_e = 563 + 22 = 585 Total sum, ''S'' = ''S''_o - ''S''_e = 1091 - 585 = 506 506 = 46 × 11 Since 506 is divisible by 11 then ''N'' is also divisible by 11. If the total sum is still too large to conveniently test for divisibility, and is longer than three digits, then the algorithm can be repeated to obtain a smaller number.

In other fields

In ''

The Book of One Thousand and One Nights ''One Thousand and One Nights'' ( ar, أَلْفُ لَيْلَةٍ وَلَيْلَةٌ, italic=yes, ) is a collection of Middle Eastern folk tales compiled in Arabic during the Islamic Golden Age. It is often known in English as the ''Arabian ...

'',

Scheherazade Scheherazade () is a major female character and the storyteller in the frame narrative of the Middle Eastern collection of tales known as the ''One Thousand and One Nights''. Name According to modern scholarship, the name ''Scheherazade'' deri ...

tells her husband the king a new story every night for 1,001 nights, staving off her execution. From this, 1001 is sometimes used as a generic term for "a very large number", starting with a large number (1000) and going beyond it: :''1001 uses for...'' :''1001 ways to...'' In

Arab The Arabs (singular: Arab; singular ar, عَرَبِيٌّ, DIN 31635: , , plural ar, عَرَب, DIN 31635: , Arabic pronunciation: ), also known as the Arab people, are an ethnic group mainly inhabiting the Arab world in Western Asia, ...

ic, this is usually phrased as "one thousand ''things'' and one ''thing''", ''e.g.'': :''The Book of One Thousand and One Nights'', in Arabic ''Alf layla wa layla'' ( ar, ألف ليلة و ليلة), literally "One thousand nights and a night". 1001 was the name of a popular British

detergent A detergent is a surfactant or a mixture of surfactants with cleansing properties when in dilute solutions. There are a large variety of detergents, a common family being the alkylbenzene sulfonates, which are soap-like compounds that are more ...

in the 1960s, supposedly with "1001 uses". In the

Mawlawiyyah The Mevlevi Order or Mawlawiyya ( tr, Mevlevilik or Mevleviyye; fa, طریقت مولویه) is a Sufi order that originated in Konya (a city now in Turkey; formerly capital of the Seljuk Sultanate) and which was founded by the followers of Jala ...

order of

Sufi Sufism ( ar, ''aṣ-ṣūfiyya''), also known as Tasawwuf ( ''at-taṣawwuf''), is a mystic body of religious practice, found mainly within Sunni Islam but also within Shia Islam, which is characterized by a focus on Islamic spirituality, ...

Islam Islam (; ar, ۘالِإسلَام, , ) is an Abrahamic religions, Abrahamic Monotheism#Islam, monotheistic religion centred primarily around the Quran, a religious text considered by Muslims to be the direct word of God in Islam, God (or ...

, a novice must complete 1001 days of prayer before becoming a ''dada'', or junior teacher of the faith. In many cases, including the title "

Thousand and One Nights ''One Thousand and One Nights'' ( ar, أَلْفُ لَيْلَةٍ وَلَيْلَةٌ, italic=yes, ) is a collection of Middle Eastern folk tales compiled in Arabic during the Islamic Golden Age. It is often known in English as the ''Arabian ...

", 1001 is meant to indicate a "big number", and need not be taken literally. A book published in 2007 titled ''40 Days & 1001 Nights'' describes a journey through the

Islamic world The terms Muslim world and Islamic world commonly refer to the Islamic community, which is also known as the Ummah. This consists of all those who adhere to the religious beliefs and laws of Islam or to societies in which Islam is practiced. In ...

. Among them are recent books aiming to introduce significant works in various fields: :''

1001 Books You Must Read Before You Die ''1001 Books You Must Read Before You Die'' is a literary reference book compiled by over one hundred literary critics worldwide and edited by Peter Boxall, Professor of English at Sussex University, with an introduction by Peter Ackroyd. Each tit ...

'' :'' 1001 Movies You Must See Before You Die'' :''

1001 Albums You Must Hear Before You Die ''1001 Albums You Must Hear Before You Die'' is a musical reference book first published in 2005 by Universe Publishing. Part of the ''1001 Before You Die'' series, it compiles writings and information on albums chosen by a panel of music critics ...

'' There are also many film titles starting with 1001. For example: :'' Bugs Bunny's 3rd Movie: 1001 Rabbit Tales'' The NBA Draft Lottery uses a lottery with 1,001 combinations by selecting four balls out of 14, then disregards the combination 11, 12, 13 and 14 to produce 1,000 outcomes. 1001 was a hidden track on the Australian release of ''

Two Shoes ''Two Shoes'' is the second studio album by Australian ska-jazz band The Cat Empire, which was issued on 19 April 2005. It is the follow-up to their successful self-titled first album. It was recorded in November to December 2004 in Havana, C ...

'', the second album by

The Cat Empire The Cat Empire are an Australian jazz/funk band, formed in Melbourne, Victoria, in 1999. For most of the band's duration, the core members were Felix Riebl (lead vocals, percussion), Harry James Angus (trumpet, vocals), Will Hull-Brown (drums), ...

Buckminster Fuller Richard Buckminster Fuller (; July 12, 1895 – July 1, 1983) was an American architect, systems theorist, writer, designer, inventor, philosopher, and futurist. He styled his name as R. Buckminster Fuller in his writings, publishing more t ...

called 1001 a Scheherazade number in his book ''Synergetics'', since Scheherazade was the name of the story-telling wife in ''

''.

References

{{DEFAULTSORT:1001 (Number) Integers