| ||||
---|---|---|---|---|
Cardinal | thirteen | |||
Ordinal | 13th (thirteenth) | |||
Numeral system | tredecimal | |||
Factorization | prime | |||
Prime | 6th | |||
Divisors | 1, 13 | |||
Greek numeral | ΙΓ´ | |||
Roman numeral | XIII | |||
Binary | 11012 | |||
Ternary | 1113 | |||
Senary | 216 | |||
Octal | 158 | |||
Duodecimal | 1112 | |||
Hexadecimal | D16 | |||
Hebrew numeral | י"ג | |||
Babylonian numeral | 𒌋𒐗 |
13 (thirteen) is the natural number following 12 and preceding 14.
Folklore surrounding the number 13 appears in many cultures around the world: one theory is that this is due to the cultures employing lunar-solar calendars (there are approximately 12.41 lunations per solar year, and hence 12 "true months" plus a smaller, and often portentous, thirteenth month). This can be witnessed, for example, in the "Twelve Days of Christmas" of Western European tradition. [1]
The number 13 is a prime number, happy number [2] and a lucky number. [3] It is a twin prime with 11, as well as a cousin prime with 17. It is the second of only 3 Wilson primes: 5, 13, and 563. A 13-sided regular polygon is called a tridecagon.
Multiplication | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 50 | 100 | 1000 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
(13)x | 13 | 26 | 39 | 52 | 65 | 78 | 91 | 104 | 117 | 130 | 143 | 156 | 169 | 182 | 195 | 208 | 221 | 234 | 247 | 260 | 273 | 286 | 299 | 312 | 325 | 650 | 1300 | 13000 |
Division | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
13 ÷ x | 13 | 6.5 | 4.3 | 3.25 | 2.6 | 2.16 | 1.857142 | 1.625 | 1.4 | 1.3 | 1.18 | 1.083 | 1 | 0.9285714 | 0.86 |
x ÷ 13 | 0.076923 | 0.153846 | 0.230769 | 0.307692 | 0.384615 | 0.461538 | 0.538461 | 0.615384 | 0.692307 | 0.769230 | 0.846153 | 0.923076 | 1 | 1.076923 | 1.153846 |
Exponentiation | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
---|---|---|---|---|---|---|---|---|---|---|---|
13x | 13 | 169 | 2197 | 28561 | 371293 | 4826809 | 62748517 | 815730721 | 10604499373 | 137858491849 | 1792160394037 |
x13 | 1 | 8192 | 1594323 | 67108864 | 1220703125 | 13060694016 | 96889010407 | 549755813888 | 2541865828329 | 10000000000000 | 34522712143931 |
In Germany, according to an old tradition, 13 (dreizehn), as the first compound number, was the first number written in digits; the numbers 0 (null) through 12 (zwölf) were spelled out. The Duden (the German standard dictionary) now calls this tradition (which was actually never written down as an official rule) outdated and no longer valid, but many writers still follow it. [4]
Thirteen is one of two numbers within the teen numerical range (13–19), along with fifteen, not derived by cardinal numeral (three) and the teen suffix; instead, it is derived from the ordinal numeral (third).
In Shia, 13 signifies the 13th day of the month of Rajab (the Lunar calendar), which is the birth of Imam Ali. 13 also is a total of 1 Prophet and 12 Shia Imams in the Islamic School of Thought.
Christianity
In all branches of Christianity it's said that Christ had 12 disciples, thus forming a group of 13. It's best known by the representations of the last supper.
The apparitions of the Virgin of Fátima in 1917 were claimed to occur on the 13th day of six consecutive months. [5]
In Catholic devotional practice, the number thirteen is also associated with Saint Anthony of Padua, since his feast day falls on June 13. A traditional devotion called the Thirteen Tuesdays of St. Anthony [6] involves praying to the saint every Tuesday over a period of thirteen weeks. Another devotion, St. Anthony's Chaplet, consists of thirteen decades of three beads each. [7]
According to famous Sakhi (evidence) or the story of Guru Nanak Dev Ji, when he was an accountant at a town of Sultanpur Lodhi, he was distributing groceries to people. When he gave groceries to the 13th person, he stopped because in Gurmukhi and Hindi the word 13 is called terah, which means yours. And Guru Nanak Dev Ji kept saying, "Yours, yours, yours..." remembering God. People reported to the emperor that Guru Nanak Dev Ji was giving out free food to the people. When treasures were checked, there was more money than before.
Since beginning of the Nowruz tradition, the 13th day of each new Iranian year is called Sizdah Be-dar, a festival dedicated to pranks and spending time outdoors. [8]
According to Aztec mythology, the Thirteen Heavens were formed by the gods from the head of Cipactli during creation. [9]
A common tradition in the religion Wicca holds that the number of members for a coven is ideally thirteen, though this tradition is not universal. [10]
The number 13 is considered an unlucky number in some countries. [11] The end of the Mayan calendar's 13th Baktun was superstitiously feared as a harbinger of the apocalyptic 2012 phenomenon. [12] Fear of the number 13 has a specifically recognized phobia, triskaidekaphobia, a word first recorded in 1911. [13] The superstitious sufferers of triskaidekaphobia try to avoid bad luck by keeping away from anything numbered or labelled thirteen. As a result, companies and manufacturers use another way of numbering or labelling to avoid the number, with hotels and tall buildings being conspicuous examples (thirteenth floor). [14] It is also considered unlucky to have thirteen guests at a table. Friday the 13th has been considered an unlucky day. [11]
There are a number of theories as to why the number thirteen became associated with bad luck, but none of them have been accepted as likely. [11]
In the Mayan Tzolk'in calendar, trecenas mark cycles of 13-day periods. The pyramids are also set up in 9 steps divided into 7 days and 6 nights, 13 days total.
In the standard 52-card deck of playing cards there are four suits, each of 13 ranks.
A baker's dozen, devil's dozen, [24] long dozen, or long measure is 13, one more than a standard dozen. The thirteenth loaf is called the vantage loaf because it is considered advantageous overall to get 13 loaves for the price of 12. [25]
In Arthurian legend, which was recorded in Medieval texts, King Arthur is resting in Avalon with the twelve greatest knights of the Round Table, totalling 13, and will return when his country is in peril. [26]
The Thirteen Treasures of Britain are a series of magical items listed in late Medieval texts.
The Thirteen Postures of Tai Chi are thirteen postures (consisting of Eight Gates and Five Steps) which are considered to be of fundamental importance in the practice of tai chi. [27]
In astronomy there are 13 star constellations in the zodiac (including Ophiuchus); this can be compared with astrology where there are 12 signs of the zodiac.
In Judaism, 13 signifies the age at which a boy matures and becomes a Bar Mitzvah, i.e., a full member of the Jewish faith (counts as a member of Minyan). The number of principles of Jewish faith according to Maimonides. According to Rabbinic commentary on the Torah, God has 13 Attributes of Mercy.
In a tarot card deck, XIII is the card of Death, usually picturing the Pale Horse with its rider.
Easter, also called Pascha or Resurrection Sunday, is a Christian festival and cultural holiday commemorating the resurrection of Jesus from the dead, described in the New Testament as having occurred on the third day of his burial following his crucifixion by the Romans at Calvary c. 30 AD. It is the culmination of the Passion of Jesus, preceded by Lent, a 40-day period of fasting, prayer, and penance.
The full moon is the lunar phase when the Moon appears fully illuminated from Earth's perspective. This occurs when Earth is located between the Sun and the Moon. This means that the lunar hemisphere facing Earth—the near side—is completely sunlit and appears as an approximately circular disk. The full moon occurs roughly once a month.
A month is a unit of time, used with calendars, that is approximately as long as a natural phase cycle of the Moon; the words month and Moon are cognates. The traditional concept of months arose with the cycle of Moon phases; such lunar months ("lunations") are synodic months and last approximately 29.53 days, making for roughly 12.37 such months in one Earth year. From excavated tally sticks, researchers have deduced that people counted days in relation to the Moon's phases as early as the Paleolithic age. Synodic months, based on the Moon's orbital period with respect to the Earth–Sun line, are still the basis of many calendars today and are used to divide the year.
A lunar phase or Moon phase is the apparent shape of the Moon's directly sunlit portion as viewed from the Earth. Because the Moon is tidally locked with the Earth, the same hemisphere is always facing the Earth. In common usage, the four major phases are the new moon, the first quarter, the full moon and the last quarter; the four minor phases are waxing crescent, waxing gibbous, waning gibbous, and waning crescent. A lunar month is the time between successive recurrences of the same phase: due to the eccentricity of the Moon's orbit, this duration is not perfectly constant but averages about 29.5 days.
The Metonic cycle or enneadecaeteris is a period of almost exactly 19 years after which the lunar phases recur at the same time of the year. The recurrence is not perfect, and by precise observation the Metonic cycle defined as 235 synodic months is just 2 hours, 4 minutes and 58 seconds longer than 19 tropical years. Meton of Athens, in the 5th century BC, judged the cycle to be a whole number of days, 6,940. Using these whole numbers facilitates the construction of a lunisolar calendar.
In astronomy, the new moon is the first lunar phase, when the Moon and Sun have the same ecliptic longitude. At this phase, the lunar disk is not visible to the naked eye, except when it is silhouetted against the Sun during a solar eclipse.
The Roman calendar was the calendar used by the Roman Kingdom and Roman Republic. Although the term is primarily used for Rome's pre-Julian calendars, it is often used inclusively of the Julian calendar established by the reforms of the Dictator Julius Caesar and Emperor Augustus in the late 1st century BC.
Triskaidekaphobia is fear or avoidance of the number 13. It is also a reason for the fear of Friday the 13th, called paraskevidekatriaphobia or friggatriskaidekaphobia.
Friday the 13th is considered an unlucky day in Western superstition. It occurs when the 13th day of the month in the Gregorian calendar falls on a Friday, which happens at least once every year but can occur up to three times in the same year. For example, 2015 had a Friday the 13th in February, March, and November, which will happen again in 2026. Leap years that begin on Sunday such as 2012 and 2040, also have three Friday the 13ths in January, April, and July. 2017 through 2020 had two Friday the 13ths, as did 2023; 2016, 2021, and 2022 had just one Friday the 13th, as will 2025, 2027, and 2028; 2024 will have two Friday the 13ths.
The Hindu calendar, also called Panchanga, is one of various lunisolar calendars that are traditionally used in the Indian subcontinent and Southeast Asia, with further regional variations for social and Hindu religious purposes. They adopt a similar underlying concept for timekeeping based on sidereal year for solar cycle and adjustment of lunar cycles in every three years, but differ in their relative emphasis to moon cycle or the sun cycle and the names of months and when they consider the New Year to start. Of the various regional calendars, the most studied and known Hindu calendars are the Shalivahana Shaka found in the Deccan region of Southern India and the Vikram Samvat (Bikrami) found in Nepal and the North and Central regions of India – both of which emphasize the lunar cycle. Their new year starts in spring. In regions such as Tamil Nadu and Kerala, the solar cycle is emphasized and this is called the Tamil calendar and Malayalam calendar and these have origins in the second half of the 1st millennium CE. A Hindu calendar is sometimes referred to as Panchangam (पञ्चाङ्गम्), which is also known as Panjika in Eastern India.
The ancient Egyptian calendar – a civil calendar – was a solar calendar with a 365-day year. The year consisted of three seasons of 120 days each, plus an intercalary month of five epagomenal days treated as outside of the year proper. Each season was divided into four months of 30 days. These twelve months were initially numbered within each season but came to also be known by the names of their principal festivals. Each month was divided into three 10-day periods known as decans or decades. It has been suggested that during the Nineteenth Dynasty and the Twentieth Dynasty the last two days of each decan were usually treated as a kind of weekend for the royal craftsmen, with royal artisans free from work.
The history of calendars covers practices with ancient roots as people created and used various methods to keep track of days and larger divisions of time. Calendars commonly serve both cultural and practical purposes and are often connected to astronomy and agriculture.
A blue moon refers either to the presence of a second full moon in a calendar month, to the third full moon in a season containing four, or to a moon that appears blue due to atmospheric effects.
A chronology of Jesus aims to establish a timeline for the events of the life of Jesus. Scholars have correlated Jewish and Greco-Roman documents and astronomical calendars with the New Testament accounts to estimate dates for the major events in Jesus's life.
The Buddhist calendar is a set of lunisolar calendars primarily used in Tibet, Cambodia, Laos, Myanmar, Bangladesh, India, Sri Lanka, Thailand and Vietnam as well as in Malaysia and Singapore and by Chinese populations for religious or official occasions. While the calendars share a common lineage, they also have minor but important variations such as intercalation schedules, month names and numbering, use of cycles, etc. In Thailand, the name Buddhist Era is a year numbering system shared by the traditional Thai lunar calendar and by the Thai solar calendar.
The Tibetan calendar, or the Phukpa calendar, known as the Tibetan lunar calendar, is a lunisolar calendar composed of either 12 or 13 lunar months, each beginning and ending with a new moon. A thirteenth month is added every two or three years, so that an average Tibetan year is equal to the solar year. The 15th century Phukpa calendar is the main Tibetan calendar, and the Karma Kagyu's Tsurluk calendar is also in current use. The Tibetan New Year celebration is Losar, which falls either in the months of February or March in the Gregorian calendar.
Often called lunar mansion, a lunar station or lunar house is a segment of the ecliptic through which the Moon passes in its orbit around the Earth. The concept was used by several ancient cultures as part of their calendrical system.
An ecclesiastical full moon is formally the 14th day of the ecclesiastical lunar month in an ecclesiastical lunar calendar. The ecclesiastical lunar calendar spans the year with lunar months of 30 and 29 days which are intended to approximate the observed phases of the Moon. Since a true synodic month has a length that can vary from about 29.27 to 29.83 days, the moment of astronomical opposition tends to be roughly 14.75 days after the previous conjunction of the Sun and Moon. The ecclesiastical full moons of the Gregorian lunar calendar tend to agree with the dates of astronomical opposition, referred to a day beginning at midnight at 0 degrees longitude, to within a day or so. However, the astronomical opposition happens at a single moment for the entire Earth: The hour and day at which the opposition is measured as having taken place will vary with longitude. In the ecclesiastical calendar, the 14th day of the lunar month, reckoned in local time, is considered the day of the full moon at each longitude.
In the folklore of Scandinavia, Tycho Brahe days are days judged to be especially unlucky, especially for magical work, and important business transactions. Tycho Brahe (1546–1601) was a Danish astronomer, astrologer, and alchemist and as such achieved some acclaim in popular folklore as a sage and magician.