666 (number)

In mathematics

666 is the sum of the first thirty-six natural numbers, which makes it a triangular number:

:\sum_{i=1}^{36} i = 1 + 2 + 3 + \cdots + 34 + 35 + 36 = 666.

In fact, 666 is the largest triangular number that is also a repdigit.

Since 36 is a triangular number too, 666 is a doubly triangular number. Also, 666 is the sum of squares of two consecutive Triangular numbers.

T(15+21) = 152 + 212,

which can be re-written as:

T(T5+T6) = (T5)2 + (T6)2

TT5+TT3 = (T5)2 + (TT3)2.

The difference of 21² and 15² is:

216 = 6 × 36 or 6 × 6 × 6,

Which can be expressed:

216 = (T3) × (T3)² or (TT2) × (TT2)².

666 is a congruent number, as it is possible to make a right triangle with rationally numbered side lengths whose area is 666.

The number of integers which are relatively prime to 666 is 216, \phi (666) = 216; and for an angle measured in degrees, \sin {(666^{\circ})} = \cos{(216^{\circ})} = -\tfrac {\varphi}{2} (where here \varphi is the golden ratio).{{efn|1=Other relevant trigonometric equalities include:

• ,
• , and
• .

Where, −, also equivalently .}}

666 is also the sum of the squares of the first seven primes , while the number of twin primes less than 66 + 666 is 666. :, and the 666th pair of twin primes is (47147, 47149).

A prime reciprocal magic square based on \tfrac {1}{149} in decimal has a magic constant of 666. The twelfth pair of twin primes is (149, 151), with 151 the thirty-sixth prime number.

666 is a Smith number and Harshad number in base ten. The 27th indexed unique prime in decimal features a "666" in the middle of its sequence of digits.

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

In Christian religion

Number of the beast

Main article: Number of the beast

In the Textus Receptus manuscripts of the New Testament, the Book of Revelation () cryptically asserts 666 to be "the man's number" or "the number of a man" (depending on how the text is translated) associated with the Beast, an antagonistic creature that appears briefly about two-thirds into the apocalyptic vision. Some manuscripts of the original Koine Greek use the symbols χξϛ chi xi stigma (or χξϝ with a digamma), while other manuscripts spell out the number in words.

In modern popular culture, 666 has become one of the most widely recognized symbols for the Antichrist or, alternatively Satanism. Earnest references to the number occur both among apocalypticist Christian 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 common to see the symbolic role of the integer 666 transferred to the numerical 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.

There is a broad consensus in contemporary scholarship that the number of the beast refers to the Roman emperor Nero, who reigned from 55 to 68 AD. The Greek version of his name (Νέρων Καῖσαρ, "Neron Kaisar") transliterates into Hebrew as נרון קסר (NRON QSR), and, using gematria, yields a numerical value of 666. His Latin name, "Nero Caesar", transliterated as נרו קסר (NRO QSR), produces the number 616 instead, which is also cited as the Number of the Beast in some early biblical manuscripts.

Other occurrences

• In the Bible, 666 is the number of talents of gold Solomon collected each year (see and ).
• In the Bible, 666 is the number of Adonikam's descendants who return to Jerusalem and Judah from the Babylonian exile (see ).

In other fields

• The Number of the Beast, the 1982 album by English heavy metal band Iron Maiden, references 666 in its title and the album's title song.
• Is the magic sum, or sum of the magic constants of a six by six magic square, any row or column of which adds up to 111.
• Is the sum of all the numbers on a roulette wheel (0 through 36). This is a corollary of the fact that the number is a Triangular number, as mentioned earlier.
• 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 computer virus that was discovered in 1998. It is also the name of an extension that SevenDust can add to an uninfected Macintosh.
• The number is a frequent visual element of Aryan Brotherhood tattoos.
• Aleister Crowley adopted the title "the Beast 666". As such, 666 is also associated with him, his work, and his religious philosophy of Thelema.
• Molar mass of the high-temperature superconductor YBa2Cu3O7.
• In Chinese numerology, the number is considered to be lucky and is often displayed in shop windows and neon signs. In China, 666 can mean "everything goes smoothly" (the number six has the same pronunciation as the character 溜, which means "smooth".
• Is commonly used by Internet service providers to blackhole traffic using BGP communities.
• 666 Fifth Avenue in New York City, which was bought for $1.8 billion in 2007, was the most expensive real estate deal in New York's history.

Notes

References

References

1. {{bibleverse. Revelation. 13. niv
2. Beale, Gregory K. (1999). The Book of Revelation: A Commentary on the Greek Text. Grand Rapids, Michigan: Wm. B. Eerdmans Publishing. p. 718. {{ISBN. 080282174X. Retrieved 9 July 2012.
3. "The Numerology of the Beast".
4. {{Cite OEIS. A000217. Triangular numbers
5. (6 March 2025). "Triangular Numbers With a Single Repeated Digit". Journal of Integer Sequences.
6. Math1089. (2023-05-20). "Exploring Mathematical Wonders of the Number 666".
7. {{Cite OEIS. A000010. Euler totient function phi(n): count numbers less than or equal to n and prime to n.
8. Wells, D.. (1987). "The Penguin Dictionary of Curious and Interesting Numbers". [[Penguin Books]].
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10. Bogomolny, Alexander. "Beauty and the Beast - in Trigonometry".
11. {{Cite OEIS. A024450. Sum of squares of the first n primes.
12. {{Cite OEIS. A077800. List of twin primes {p, p+2}.
13. {{Cite OEIS. A006753. Smith (or joke) numbers: composite numbers n such that sum of digits of n is equal to the sum of digits of prime factors of n (counted with multiplicity).
14. {{Cite OEIS. A005349. Niven (or Harshad, or harshad) numbers: numbers that are divisible by the sum of their digits.
15. {{Cite OEIS. A040017. Prime 3 followed by unique period primes (the period r of 1/p is not shared with any other prime)
16. "Revelation 13:18". Bible Gateway.
17. ”Nero as the Antichrist.” Encyclopaedia Romana. University of Chicago. https://penelope.uchicago.edu/encyclopaedia_romana/gladiators/nero.html. “666 (or rather DCLXVI) signifies the Antichrist because that number signifies Nero.”
18. Ehrman, Bart (2016). ‘666, The Number of the Beast.’ Bart Ehrman Blog. [https://ehrmanblog.org/666-the-number-of-the-beast/..%E2%80%9D https://ehrmanblog.org/666-the-number-of-the-beast/..”]
19. ''[[Novum Testamentum Graece]]'', Nestle and Aland, 1991, footnote to verse 13:18 of Revelation, page 659: "{{lang. grc
20. "The Other Number of the Beast".
21. "666 – professors explain Roulette and Nero in detail; numberphile.com".
22. Baer, John. (1980-09-20). "Six Won $1.2 Million in Rigged Lottery, Pa. Says". Washington Post.
23. "Detailed Analysis - Mac/Sevendust-A - Viruses and Spyware - Advanced Network Threat Protection {{!}} ATP from Targeted Malware Attacks and Persistent Threats {{!}} sophos.com - Threat Center".
24. Brook, John Lee. (June 2011). "Blood In, Blood Out: The Violent Empire of the Aryan Brotherhood". SCB Distributors.
25. "Aleister Crowley {{!}} Biography, Teachings, Reputation, & Facts {{!}} Britannica".
26. Mah, Adeline Yen. (2009). "China: Land of Dragons and Emperors". Random House Children's Books.
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29. {{IETF RFC. 7999
30. (19 June 2017). "What you need to know about 666 Fifth Avenue".