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The beast number or sign of the devil is equal to 666.[1] It is associated with Satan, evil, and bad luck in 

666

A symbolic description of 666

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."[2] 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.[3]
  • 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.

Sources Edit

  1. [1]
  2. Revelation 13:18, NIV
  3. OEIS A045914

See also Edit

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