# Simple Maths Riddle 5

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?

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!

• This must be the answer! – Matt Cremeens Dec 31 '18 at 14:59
• Yes, you got it! Prime can also mean importance, and it is so for a new year :) – TheSimpliFire Dec 31 '18 at 15:00
• Would the wording "Sum my digits and halve" be better? – greenturtle3141 Jan 1 '19 at 22:23

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: $$3^1, 3^2, 3^3, \cdots$$

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

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

• Nope (1 isn't conventionally a perfect number) ;P – TheSimpliFire Dec 31 '18 at 14:48
• Technically 1 is neither prime nor composite. – user33097 Dec 31 '18 at 15:44
• 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. – Eevee Trainer Jan 1 '19 at 10:56