13
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Here's a special one for you!

I am prime, I am composite

Sum my digits and half; I'll be perfect!

Don't multiply them, I won't yield a thing

But don't worry, it's only the beginning!

What am I?

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14
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Hoping this is good

$2019$

I am prime, I am composite

Prime as in beginning and composite as $2019 = 3\cdot673$

Sum my digits and half; I'll be perfect!

$2 + 0 + 1 + 9 = 12$, then $12/2 = 6$

Don't multiply them, I won't yield a thing

$2 \cdot 0 \cdot 1 \cdot 9 = 0$

But don't worry, it's only the beginning!

Happening around the world today!

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  • 1
    $\begingroup$ This must be the answer! $\endgroup$ – Matt Cremeens Dec 31 '18 at 14:59
  • $\begingroup$ Yes, you got it! Prime can also mean importance, and it is so for a new year :) $\endgroup$ – TheSimpliFire Dec 31 '18 at 15:00
  • 2
    $\begingroup$ Would the wording "Sum my digits and halve" be better? $\endgroup$ – greenturtle3141 Jan 1 at 22:23
2
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I'm thinking it might be

$39$

$(3+9)/2=6$, a perfect number as its factors sum to the number itself: $1+2+3=6$

$3$ is prime and $9$ is composite

Multiplying them won't yield just a thing, it yields $3\times 9=27$ things

I am a bit hung up on this but perhaps $39$ is the beginning of a sequence where these rules hold true (i.e., it's the smallest number produced by these rules). Or perhaps it's the first two of this series: $3^1, 3^2, 3^3, \cdots$

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  • 2
    $\begingroup$ (3+8)/2 is not 6, but 5.5 $\endgroup$ – SPK.z Dec 31 '18 at 14:46
  • $\begingroup$ Nope, unfortunately, but good attempt! $\endgroup$ – TheSimpliFire Dec 31 '18 at 14:47
  • 1
    $\begingroup$ @SPK.z I can't believe I made that mistake. I'll edit. $\endgroup$ – Matt Cremeens Dec 31 '18 at 14:48
2
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Partial:

Are you

1?

I am prime, I am composite

Some say 1 is prime, some say it is composite

Sum my digits and half; I'll be perfect!

? Perfect number? Perhaps not

Don't multiply them, I won't yield a thing

any n*1 yield n

But don't worry, it's only the beginning!

beginning of natural numbers

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  • $\begingroup$ Nope (1 isn't conventionally a perfect number) ;P $\endgroup$ – TheSimpliFire Dec 31 '18 at 14:48
  • 2
    $\begingroup$ Technically 1 is neither prime nor composite. $\endgroup$ – tilper Dec 31 '18 at 15:44
  • 1
    $\begingroup$ To note, a "perfect number" is a number whose factors sum to twice that number, or one whose factors (excluding itself) sum to the number itself. $\endgroup$ – Eevee Trainer Jan 1 at 10:56

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