666 (number)

# 666 (number)

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 666 CardinalCardinal numberIn mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality of sets. The cardinality of a finite set is a natural number – the number of elements in the set. The transfinite cardinal numbers describe the sizes of infinite... Six hundred and sixty-six OrdinalOrdinal numberIn set theory, an ordinal number, or just ordinal, is the order type of a well-ordered set. They are usually identified with hereditarily transitive sets. Ordinals are an extension of the natural numbers different from integers and from cardinals... 666th FactorizationFactorizationIn mathematics, factorization or factoring is the decomposition of an object into a product of other objects, or factors, which when multiplied together give the original... Greek numeral Roman numeral DCLXVI Chinese numeral 六百六十六 BinaryBinary numeral systemThe binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2... 1010011010 OctalOctalThe octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Numerals can be made from binary numerals by grouping consecutive binary digits into groups of three... 1232 HexadecimalHexadecimalIn mathematics and computer science, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, and A, B, C, D, E, F to represent values ten to fifteen... 29A Base12 476, i.e. 04 07 06 Base32 KQ Base36 II Base60 11 06

666 (six hundred and sixty-six) is the natural number
Natural number
In mathematics, the natural numbers are the ordinary whole numbers used for counting and ordering . These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively...

following 665 and preceding 667.

## In mathematics

666 is the sum of the first 36 natural numbers (i.e. ), and thus a triangular number
Triangular number
A triangular number or triangle number numbers the objects that can form an equilateral triangle, as in the diagram on the right. The nth triangle number is the number of dots in a triangle with n dots on a side; it is the sum of the n natural numbers from 1 to n...

.

Since 36
36 (number)
36 is the natural number following 35 and preceding 37.- In mathematics :36 is both the square of 6 and a triangular number, making it a square triangular number...

is both square
Square number
In mathematics, a square number, sometimes also called a perfect square, is an integer that is the square of an integer; in other words, it is the product of some integer with itself...

and triangular, 666 is the sixth number of the form and the eighth number of the form (doubly triangular numbers) .

The number of prime numbers up to 666 is 121, which is the square of 11, which is the number of prime numbers up to 36.

666 is the sum of the squares of the first 7 prime numbers: 4+9+25+49+121+169+289=666.

666 is an abundant number.

The harmonic mean
Harmonic mean
In mathematics, the harmonic mean is one of several kinds of average. Typically, it is appropriate for situations when the average of rates is desired....

of the decimal digit
Numerical digit
A digit is a symbol used in combinations to represent numbers in positional numeral systems. The name "digit" comes from the fact that the 10 digits of the hands correspond to the 10 symbols of the common base 10 number system, i.e...

s of 666 is (trivially — all repdigit
Repdigit
In recreational mathematics, a repdigit is a natural number composed of repeated instances of the same digit, most often in the decimal numeral system....

natural numbers have this property) an integer
Integer
The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...

: 3/(1/6 + 1/6 + 1/6) = 6, making 666 the 54th number with this property.

In base 10
Radix
In mathematical numeral systems, the base or radix for the simplest case is the number of unique digits, including zero, that a positional numeral system uses to represent numbers. For example, for the decimal system the radix is ten, because it uses the ten digits from 0 through 9.In any numeral...

, 666 is a repdigit
Repdigit
In recreational mathematics, a repdigit is a natural number composed of repeated instances of the same digit, most often in the decimal numeral system....

(and therefore a palindromic number
Palindromic number
A palindromic number or numeral palindrome is a 'symmetrical' number like 16461, that remains the same when its digits are reversed. The term palindromic is derived from palindrome, which refers to a word like rotor that remains unchanged under reversal of its letters...

) and a Smith number
Smith number
A Smith number is a composite number for which, in a given base , the sum of its digits is equal to the sum of the digits in its prime factorization. For example, 378 = 2 × 3 × 3 × 3 × 7 is a Smith number since 3 + 7 + 8 =...

. A prime reciprocal magic square
Prime reciprocal magic square
A prime reciprocal magic square is a magic square using the decimal digits of the reciprocal of a prime number.Consider a number divided into one, like 1/3 or 1/7. In base ten, the remainder, and so the digits, of 1/3 repeats at once: 0·3333... However, the remainders of 1/7 repeat over six, or...

based on 1/149 in base 10 has a magic total of 666.

The Roman numeral for 666, DCLXVI, has exactly one occurrence of all symbols whose value is less than 1000 (D=500, C=100, L=50, X=10, V=5, I=1).

666 is a member of the indices of prime Pandovan numbers
Padovan sequence
The Padovan sequence is the sequence of integers P defined by the initial valuesP=P=P=1,and the recurrence relationP=P+P.The first few values of P are...

: 3, 4, 5, 7, 8, 14, 19, 30, 37, 84, 128, 469, 666, 1262, 1573, 2003, 2210, ... .

The sine
Sine
In mathematics, the sine function is a function of an angle. In a right triangle, sine gives the ratio of the length of the side opposite to an angle to the length of the hypotenuse.Sine is usually listed first amongst the trigonometric functions....

of the angle 666° multiplied by -2 is equal to the golden ratio
Golden ratio
In mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The golden ratio is an irrational mathematical constant, approximately 1.61803398874989...

:

## The Number of the Beast

In the New Testament
New Testament
The New Testament is the second major division of the Christian biblical canon, the first such division being the much longer Old Testament....

, the Book of Revelation
Book of Revelation
The Book of Revelation is the final book of the New Testament. The title came into usage from the first word of the book in Koine Greek: apokalupsis, meaning "unveiling" or "revelation"...

cryptically asserts 666 to be "the number of a man," associated with the beast
The Beast (Bible)
The Beast of Revelation, may refer to two beasts in the apocalyptic visions by John of Patmos, as written in the Book of Revelation. The first beast comes from "out of the sea". The second beast comes from "out of the earth" and directs all peoples of the earth to worship the first. This first...

, an antagonistic creature that appears briefly about two-thirds into the apocalyptic vision.

In modern popular culture, 666 has become one of the most widely recognized symbols for the Antichrist
Antichrist
The term or title antichrist, in Christian theology, refers to a leader who fulfills Biblical prophecies concerning an adversary of Christ, while resembling him in a deceptive manner...

or, alternatively, the Devil
Devil in Christianity
In mainstream Christianity, the Devil is named Satan, and sometimes Lucifer. He is a fallen angel who rebelled against God. He is often identified as the serpent in the Garden of Eden, whose persuasions led to original sin and the need for Jesus Christ's redemption...

. Earnest references to the number occur both among apocalypticist
Apocalypticism
Apocalypticism is the religious belief that there will be an apocalypse, a term which originally referred to a revelation of God's will, but now usually refers to belief that the world will come to an end time very soon, even within one's own lifetime...

Christian
Christian
A Christian is a person who adheres to Christianity, an Abrahamic, monotheistic religion based on the life and teachings of Jesus of Nazareth as recorded in the Canonical gospels and the letters of the New Testament...

groups and in explicitly anti-Christian subcultures.
References in contemporary Western art or literature are, more likely than not, intentional references to the Beast symbolism. Such popular references are therefore too numerous to list.

It is not uncommon to see the symbolic role of the integer 666 transferred to the digit sequence 6-6-6. Some people take the Satanic associations of 666 so seriously that they actively avoid things related to 666 or the digits 6-6-6. This is known as hexakosioihexekontahexaphobia
Hexakosioihexekontahexaphobia
Hexakosioihexekontahexaphobia is the fear...

.
• In the Bible
Bible
The Bible refers to any one of the collections of the primary religious texts of Judaism and Christianity. There is no common version of the Bible, as the individual books , their contents and their order vary among denominations...

, is the number of talents of gold Solomon
Solomon
Solomon , according to the Book of Kings and the Book of Chronicles, a King of Israel and according to the Talmud one of the 48 prophets, is identified as the son of David, also called Jedidiah in 2 Samuel 12:25, and is described as the third king of the United Monarchy, and the final king before...

collected each year (see ).
• In the Bible, is the number of Adonikam
Adonikam
Adonikam - whom the Lord sets up, one of those "which came with Zerubbabel". His "children," or retainers, to the number of 666,came up to Jerusalem .-External links:*...

's descendants who return to Jerusalem and Judah
Judea
Judea or Judæa was the name of the mountainous southern part of the historic Land of Israel from the 8th century BCE to the 2nd century CE, when Roman Judea was renamed Syria Palaestina following the Jewish Bar Kokhba revolt.-Etymology:The...

from the Babylonian exile (see ).
• In Kabbalistic Judaism the number represents the creation and perfection of the world. The world was created in 6 days, and there are 6 cardinal directions (North, South, East, West, Up, Down).

## In other fields

• is the magic sum, or sum of the magic constant
Magic constant
The magic constant or magic sum of a magic square is the sum of numbers in any row, column, and diagonal of the magic square. For example, the magic square shown below has a magic constant of 15....

s of a six by six magic square
Magic square
In recreational mathematics, a magic square of order n is an arrangement of n2 numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. A normal magic square contains the integers from 1 to n2...

, any row or column of which adds up to 111.
• is the sum of all the numbers on a roulette
Roulette
Roulette is a casino game named after a French diminutive for little wheel. In the game, players may choose to place bets on either a single number or a range of numbers, the colors red or black, or whether the number is odd or even....

wheel (1 through to 36).
• was a winning lottery number in the 1980 Pennsylvania Lottery scandal, in which equipment was tampered to favor a 4 or 6 as each of the three individual random digits.
• was the original name of the Macintosh SevenDust
SevenDust (computer virus)
SevenDust was a computer virus that affected computers running certain versions of Mac OS. It was discovered in 1998. It was originally referred to as 666.- External links :*, by Symantec*, by McAfee*, by McAfee...

computer virus that was discovered in 1998.
• The number is a frequent visual element of Aryan Brotherhood
Aryan Brotherhood
The Aryan Brotherhood, also known as The Brand, the AB, or the One-Two, is a white supremacist prison gang and organized crime syndicate in the United States with about 20,000 members in and out of prison...

tattoo
Tattoo
A tattoo is made by inserting indelible ink into the dermis layer of the skin to change the pigment. Tattoos on humans are a type of body modification, and tattoos on other animals are most commonly used for identification purposes...

s.
• Aleister Crowley adopted the namesake 'the Great Beast 666'. As such, 666 is also associated with him, his work, and his religious philosophy of Thelema
Thelema
Thelema is a religious philosophy that was established, defined and developed by the early 20th century British writer and ceremonial magician, Aleister Crowley. He believed himself to be the prophet of a new age, the Æon of Horus, based upon a religious experience that he had in Egypt in 1904...

.