What are some interesting mathematical facts about the number 666?

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SUMMARY

The number 666 exhibits several intriguing mathematical properties. It can be expressed as 2(012) + 20(12) + 201(2) = 666. Additionally, 666 is the sum of the first seven prime numbers and satisfies the Euler totient function where φ(666) = 6.6.6. The sum of integers from 1 to 6.6 equals 666, and φ is also represented as -2sin(666°) = -2cos(6.6.6°). Notably, the original "number of the beast" was 616, not 666.

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  • Understanding of prime numbers
  • Familiarity with the Euler totient function
  • Basic knowledge of trigonometric functions
  • Awareness of mathematical series and summations
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  • Explore the properties of prime numbers and their significance in number theory
  • Study the Euler totient function and its applications in cryptography
  • Learn about trigonometric identities and their relationships to angles
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kraphysics
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2(012) + 20(12) + 201(2)= 666!

I don't mean to start a discussion on 2012 or on religious topics, I just thought that was cool.
 
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Other cool thingies:

- 666 is the number of the first seven primes
- [tex]\phi(666)=6.6.6[/tex], where phi is the Euler totient function
- [tex]\sum_{i=1}^{6.6}{i}=666[/tex]
- [tex]\phi=-2\sin(666^\circ)=-2\cos(6.6.6^\circ)[/tex] where phi is the golden ratio
- The first [tex]12^2[/tex] numbers of the fractional expansion of pi sum up to 666.

Also note that the original number of the beast was reportedly 616, and not 666...
 

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