More Perfect

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(C)Copyright 2019, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

Tell it to the Mersennes!

I might reuse that line in a future comic. The Mersenne first appeared back in Comic #70 back in 2008. Their uniforms are a little lighter now.

And as discussed in this blog post from a few days ago, every known perfect number is a multiple of a Mersenne prime, and the other number is a power of 2.

Unfortunately for Rudy (8's proper name is Rudolph), 8 is not one of the powers of 2 have creates a perfect number. The form is (2^{n - 1})(2ⁿ - 1). Since 8 = 2³, n = 4, but 2⁴ - 1 is not prime, but the product of (2² + 1)(2² - 1). That is to say, that 16 - 1 = 15, which is the product of 5 times 3.

Final note: I was going to state "a more perfect union", in a Constitutional allusion, but I figured folks would tell me that union would imply addition. Or something other than what I intended. So I'll save that for some other time.




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