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| 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,mi | |||
| Roman numeral (unicode) | MI, mi, ↀI | |||
| Unicode symbol | ↀI | |||
| Greekprefix | chilia-ena- | |||
| Binary | 11111010012 | |||
| Ternary | 11010023 | |||
| Senary | 43456 | |||
| Octal | 17518 | |||
| Duodecimal | 6B512 | |||
| Hexadecimal | 3E916 | |||
| Tamil | ௲௧ | |||
| Chinese | 千一 | |||
| Punjabi | ੧੦੦੧ | |||
1001 is thenatural number following1000 and preceding1002.
One thousand and one is asphenic number, apentagonal number, apentatope number[1] and the first four-digitpalindromic 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 thedivisibility rule for 11 using the property 10 ≡ -1 (mod 11). The two properties of 1001 are
1001 = 7 × 11 × 13 in prime factors103 ≡ -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 13iff the result of the summation is divisible by 7, 11 or 13 respectively.[2][3]
Example:
Number under test,N = 22 872 563 219Sum of odd groups,So = 219 + 872 = 1091Sum of even groups,Se = 563 + 22 = 585Total sum,S =So -Se = 1091 - 585 = 506506 = 46 × 11
Since 506 is divisible by 11 thenN 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.
On theWindows calculator, 1001 is the smallest positive integer whosereciprocal is automatically displayed in scientific notation. On Windows Calculator, numbers larger than 1032 and non-terminating decimals smaller than 0.001 or 10−3 are always displayed exponentially.
Any three-digit number multiplied by 1001 will replicate itself alongside resulting in a six-digit number (for example 382 multiplied by 1001 gives 382382). Any such six-digit number will always be divisible by 7, 11 and 13, although it is not obvious if one does not know the factors of 1001. This forms the basis of a common arithmetic trick.
InThe 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 asa generic term for "a very large number", starting with a large number (1000) and going beyond it:
InArabic, this is usually phrased as "one thousandthings and onething",e.g.:
1001 was the name of a popular Britishdetergent in the 1960s, supposedly with "1001 uses".
In theMawlawiyyah order ofSufiIslam, a novice must complete 1001 days of prayer before becoming adada, 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 titled40 Days & 1001 Nights describes a journey through theIslamic 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:
TheNBA 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 ofTwo Shoes, the second album bythe Cat Empire.
Buckminster Fuller called 1001 aScheherazade number in his bookSynergetics, since Scheherazade was the name of the story-telling wife inThe Book of One Thousand and One Nights.
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