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The beast number or sign of the devil is equal to 666. It is associated with Satan, evil, and bad luck in

Western numerology.

The number's origin is in Revelation 13:18 from the Christian Bible: "This calls for wisdom. Let the person who has insight calculate the number of the beast, for it is the number of a man. That number is 666." Some translations give 616.

A number with 666 digits is called an apocalypse number, and a number of the form 2n containing 666 in its decimal expansion is called an apocalyptic number.

## Properties Edit

Its prime factorization is 2 × 32 × 37.

A popular phenomenon in recreational mathematics is discovering "unusual" properties of 666 (mostly coincidental). Here are some of them:

• 666 is the sum of the squares of the first seven primes: 22 + 32 + 52 + 72 + 112 + 132 + 172 = 666
• 666 = DCLXVI, using all of the Roman numerals except for M in descending order. For the same reason, the six Japanese yen coins sum to ¥666.
• 666 is the increasing and decreasing sum of the first six perfect cubes: 13 + 23 + 33 + 43 + 53 + 63 + 53 + 43 + 33 + 23 + 13 = 666
• φ(666) = 6 · 6 · 6, where φ represents Euler's totient function.
• 666 is the alternating sum of the first three sixth powers: 16 - 26 + 36.
• 666 is the 36th (6 · 6th) triangular number.
• Thus, it is the sum of the numbers on the American roulette wheel. 00, 0, 1, 2, 3, ... 35, 36.
• It is the largest repdigit triangular number.
• 222,111 is the 666th triangular number, and the 222,111th triangular number is 24,666,759,216.
• There are exactly six digit 6's in the decimal expansion of 6666: 87,266,061,345,623,616.
• Similarly, there are 2 · 6 (12) digit 6's in the decimal expansion of 66666: 2,235,111,150,895,389,301,249,381,342,232,951,352,130,031,828,640,647,616,754,238,557,881,163,071,896,851,147,531,724,784,530,814,582,097,445,922,881,737,078,370,567,562,092,223,091,453,615,905,548,102,178,073,175,097,305,670,733,077,683,179,094,016.
• There are three ordered pandigital sums that produce 666, two increasing and one decreasing: 1 + 2 + 3 + 4 + 567 + 89 = 123 + 456 + 78 + 9 = 9 + 87 + 6 + 543 + 21 = 666
• The first 144 (122) digits of pi add up to 666.
• The sine of the angle 666° multiplied by -2 is equal to the golden ratio.
• The sum of the first nine digits of pi in groups of three is: 314 + 159 + 265 = 666 + 66 + 6
• Similarly, if you reverse the digits, you get: 562 + 951 + 413 = 666 + 666 + 666 - 66 - 6
• Interestingly, by turning 666 upside down, you get 999, the UK official emergency number.

It is also the prize for 4 correct final digits in the German lottery Super 6 in euros.

## See also Edit

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