Bob lures the Internet into a Big Kult

Red = Blue + Green
The Master proved it.
Want the t-shirt?
Solve the PizzaQ.

Are you getting this? I'll try to make it short and skip everything but The PizzaQ.

Vleeptron is trying to Lure You Into A Kult.

There. I've said it out loud, up front.

Most Kults, a pretty young blonde girl with freckles and a great big smile approaches you in the mall and asks if you want to go to a party tonight. And you, being a moron, say Okay. You can kiss your Hyundai goodbye.

Not so easy to get into My Kult. I'm not smiling, I don't have freckles, I don't want your Hyundai, and odds are we won't let you into our Kult because you're ... well, you're not smart enough. Or maybe you're smart, but you're also lazy.

And no Kult Party tonight. Maybe later, after you solve the very simple and straightforward PizzaQ.

If you want to Join My Kult, you will probably spend the next fortnight drinking Jolt Cola and Programming Your Computer. (It makes as much sense as the Karate Kid washing the Master's car for a week.)

Make that a Fortnight and One Night if you don't know any programming languages. Find the nice boy's QuickbasicCafe or QBCafe or whatever he calls it, I think he's in DE, and download Quickbasic for free. It was designed so that you could program your computer after just one night's study.

Beginner's
All-purpose
Symbolic
Instruction
Code

If you already know C++ or Java or Forth or LisP then it will only take you two weeks. Unless you're some bad combo of Not Too Bright and Pretty Lazy.

Hey! That's a really bad-ass Ph.D. in Emily Dickinson's Poetry you're waving in my face! And from a REALLY prestigious and fully accredited expensive private university! I'm impressed! Do you like this one?

I'm Nobody! Who are you?
Are you -- Nobody -- Too?
Then there's a pair of us!
Don't tell! they'd advertise -- you know!

How dreary -- to be -- Somebody!
How public -- like a Frog --
To tell one's name -- the livelong June --
To an admiring Bog!

Okay, back to How To Join My Kult, and Win The Pizza.

Okay, you remember how to do stuff like

2 x 32 = 64

and

512 - 1 = 511

? Did you get as far as long division? Well, that's all the Advanced Mathematics you need for this PizzaQ. If you got through 7th grade before you dropped math and started specializing in Haiku, you're set.

Maybe you need to take one Square Root, but it doesn't have to be Exact, it can be Just Ballpark.

The addition, subtraction, multiplication and long division, with Remainder, they all have to be Exact, Perfect, every damn digit, no roundoffs, no approximations. Perfection is what My Kult is All About.

So look. First compute

2 x 2 x 2 x 2 x 2 x ........

until you've managed to compute 2 to the 67th power.

Then subtract one.

Man, that's a whomp-ass big number!

Is it a Prime Number? Which can't be evenly divided by anything but 1 and the whomp-ass big number itself.

If it can be evenly divided by some other number,
it's a Composite.

So is (2^67) - 1 a Prime or a Composite?

Well, okay, we'll give you a Big Kult Shortcut:
It's a Composite.

So: What numbers divide evenly into it?
What are the Prime Factors of (2^67) - 1 ?

That's all you need to do to Join My Kult (and win some Pizza).

But of course:

NO GOOGLING.
VLEEPTRON HONOR SYSTEM.
NO HELP.
YOU GOT TO GET THE ANSWER
ALL BY YOURSELF.

But you CAN ask Your Silicon Friend to help you. You can teach your Silicon Friend how to do all the multiplication and the subtraction and then a shitload of nasty long divisions.

Here's a rather small, modest example.

2^29 = 2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2

2^29 =
(2x2x2x2)x(2x2x2x2)x(2x2x2x2)x(2x2x2x2)
x(2x2x2x2)x(2x2x2x2)x(2x2x2x2)x2

2^29 = 256 x 256 x 256 x 256 x 256 x 256 x (256 x 2)

2^29 = 65536 x 65536 x 65536 x 512

(Now use built-in Windows calculator.)

2^29 = 144115188075855872

(2^29) - 1 = 144115188075855871

Is this rather small, modest number a Prime?

If it's a Composite,
what smaller numbers can it be evenly divided by?

Without even a pencil and paper, you can do
The Rule Of Threes in your head and you can see
that it can't be evenly divided by 3.

And obviously 5 can't evenly divide into it.

Next Prime is 7.

Holy crap! We got a break!

7 x 20587884010836553 = 144115188075855871

So (2^29) - 1 = 144115188075855871

is a Composite, and it's evenly divisible
by 7 and 20587884010836553

If that had been the PizzaQ, you would now be eating Pizza, and wearing the t-shirt of My Kult.

But the PizzaQ wants to know if

(2^67) - 1 is Prime

and if it's not Prime,
what smaller number can it be evenly divided by?

Not so small and modest a number.

But you don't have to spend a year computing it and trying to divide it by all the Primes in low-to-high order.

You can teach your Silicon Pal to do all the nasty horrible computations for you. And your Silicon Pal doesn't make mistakes! (Like you'd make if you tried to do it with just pencil and paper.)

Let's get some answers here.
Haven't you ever wanted to join a Kult?