| ||||
|---|---|---|---|---|
| Cardinal | one thousand [and] one | |||
| Ordinal | 1001st (one thousand [and] first) | |||
| Factorization | 7 × 11 × 13 | |||
| Divisors | 1, 7, 11, 13, 77, 91, 143, 1001 | |||
| Greek numeral | ,ΑΑ´ | |||
| Roman numeral | MI | |||
| Roman numeral (unicode) | MI, mi, ↀI | |||
| Unicode symbol(s) | ↀI | |||
| Greek prefix | chilia-ena- | |||
| Binary | 11111010012 | |||
| Ternary | 11010023 | |||
| Senary | 43456 | |||
| Octal | 17518 | |||
| Duodecimal | 6B512 | |||
| Hexadecimal | 3E916 | |||
| Tamil | ௲௧ | |||
| Chinese | 千一 | |||
| Punjabi | ੧੦੦੧ | |||
1001 is the natural number following 1000 and preceding 1002.
One thousand and one is a sphenic number, a pentagonal number, a pentatope number [1] and the first four-digit palindromic number. Scheherazade numbers always have 1001 as a factor.
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 the result of the summation is divisible by 7, 11 or 13 respectively. [2] [3]
Example:
Number under test, N = 22 872 563 219 Sum of odd groups, So = 219 + 872 = 1091 Sum of even groups, Se = 563 + 22 = 585 Total sum, S = So - Se = 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 The Book of One Thousand and One Nights , Scheherazade 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:
In Arabic, this is usually phrased as "one thousand things and one thing", e.g.:
1001 was the name of a popular British detergent in the 1960s, supposedly with "1001 uses".
In the Mawlawiyyah order of Sufi Islam, 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", 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. [4]
Among them are recent books aiming to introduce significant works in various fields:
There are also many film titles starting with 1001. For example:
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 , the second album by the Cat Empire.
Buckminster Fuller called 1001 a Scheherazade number in his book Synergetics, since Scheherazade was the name of the story-telling wife in The Book of One Thousand and One Nights .
A senary numeral system has six as its base. It has been adopted independently by a small number of cultures. Like the decimal base 10, the base is a semiprime, though it is unique as the product of the only two consecutive numbers that are both prime. As six is a superior highly composite number, many of the arguments made in favor of the duodecimal system also apply to the senary system.
One Thousand and One Nights is a collection of Middle Eastern folktales compiled in the Arabic language during the Islamic Golden Age. It is often known in English as the Arabian Nights, from the first English-language edition, which rendered the title as The Arabian Nights' Entertainment.
In mathematics, Pascal's triangle is an infinite triangular array of the binomial coefficients which play a crucial role in probability theory, combinatorics, and algebra. In much of the Western world, it is named after the French mathematician Blaise Pascal, although other mathematicians studied it centuries before him in Persia, India, China, Germany, and Italy.
A palindromic number is a number that remains the same when its digits are reversed. In other words, it has reflectional symmetry across a vertical axis. The term palindromic is derived from palindrome, which refers to a word whose spelling is unchanged when its letters are reversed. The first 30 palindromic numbers are:
3 (three) is a number, numeral and digit. It is the natural number following 2 and preceding 4, and is the smallest odd prime number and the only prime preceding a square number. It has religious and cultural significance in many societies.
In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals 32 and can be written as 3 × 3.
In combinatorics, double counting, also called counting in two ways, is a combinatorial proof technique for showing that two expressions are equal by demonstrating that they are two ways of counting the size of one set. In this technique, which van Lint & Wilson (2001) call "one of the most important tools in combinatorics", one describes a finite set from two perspectives leading to two distinct expressions for the size of the set. Since both expressions equal the size of the same set, they equal each other.
Scheherazade is a major character and the storyteller in the frame narrative of the Middle Eastern collection of tales known as the One Thousand and One Nights.
60 (sixty) is the natural number following 59 and preceding 61. Being three times 20, it is called threescore in older literature.
A power of two is a number of the form 2n where n is an integer, that is, the result of exponentiation with number two as the base and integer n as the exponent.
1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.
In arithmetic and algebra, the cube of a number n is its third power, that is, the result of multiplying three instances of n together. The cube of a number or any other mathematical expression is denoted by a superscript 3, for example 23 = 8 or (x + 1)3.
In mathematics, a harshad number in a given number base is an integer that is divisible by the sum of its digits when written in that base. Harshad numbers in base n are also known as n-harshad numbers. Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. The word "harshad" comes from the Sanskrit harṣa (joy) + da (give), meaning joy-giver. The term "Niven number" arose from a paper delivered by Ivan M. Niven at a conference on number theory in 1977.
A divisibility rule is a shorthand and useful way of determining whether a given integer is divisible by a fixed divisor without performing the division, usually by examining its digits. Although there are divisibility tests for numbers in any radix, or base, and they are all different, this article presents rules and examples only for decimal, or base 10, numbers. Martin Gardner explained and popularized these rules in his September 1962 "Mathematical Games" column in Scientific American.
100,000 (one hundred thousand) is the natural number following 99,999 and preceding 100,001. In scientific notation, it is written as 105.
The Luhn mod N algorithm is an extension to the Luhn algorithm that allows it to work with sequences of values in any even-numbered base. This can be useful when a check digit is required to validate an identification string composed of letters, a combination of letters and digits or any arbitrary set of N characters where N is divisible by 2.
In number theory, Lucas's theorem expresses the remainder of division of the binomial coefficient by a prime number p in terms of the base p expansions of the integers m and n.
One Hundred and One Nights is a book of Arabic literature consisting of twenty stories, which presents many similarities to the more famous One Thousand and One Nights.
