Morning Mathematical Monsters & Maniacs!

(Today’s post is sponsored by the letter “M”)

Hi, I’m Super Safi and you may remember me from such stats and strategy posts as Kwik-E-Mart Farming and the advanced losing-to-win Superheroes battle strategy.

Over the past 600+ episodes, The Simpsons has taken us on an amazing mathematical journey involving fractions, probability, Fermat’s last theorem, and hundreds of other aspects from the wonderful world off mathematics.

And what better way to start your week, then by discussing math Monday morning?

This week, we’re going to step away from the TV show and talk about a mathematical number relevant to the game.

As many of you have often asked, there is an upper limit to how much in-game cash you can accumulate. That limit is $4,294,967,295.

Once you reach $4,294,967,295, some fun dialogue pops up between Prof. Frink and Homer and the in-game cash turns red. It does not increase beyond this point. But why is this number significant?

**4,294,967,295**

4,294,967,295 is equal to 2^{32} − 1. As you may recall from three weeks ago when we discussed Mersenne Primes, Mersenne Primes also come in the form 2^{n} − 1. However, 4,294,967,295 is not a Mersenne Prime, as it has a factorization of 3 x 5 x 17 x 257 x 65,537.

These 5 factors may look familiar to some of you, as these are the 5 Fermat prime numbers. Fermat primes were first studies by the French giant of mathematics Pierre de Fermat (pictured below).

Fermat believed that F*(n*) = 2^{2^n} + 1 were prime numbers. He proved that the first 5 such numbers were indeed prime:

F(0) = 2^{2^0} + 1 = 2^{1} + 1 = 2 + 1 = 3

F(1) = 2^{2^1} + 1 = 2^{2} + 1 = 4 + 1 = 5

F(2) = 2^{2^2} + 1 = 2^{4} + 1 = 16 + 1 = 17

F(3) = 2^{2^3} + 1 = 2^{8} + 1 = 256 + 1 = 257

F(4) = 2^{2^4} + 1 = 2^{16} + 1 = 65,536 + 1 = 65,537

In 1732, Swiss mathematician Leonhard Euler proved that F(5) is not a prime number. Over the past 300 years, several other Fermat numbers have been shown not to be primes. To date, only these first 5 numbers proved by Fermat have been shown to be Fermat primes.

Aside from being factorized by the 5 Fermat primes, 4,294,967,295 is important in the world of computing. The number 4,294,967,295, equivalent to the hexadecimal value FFFF,FFFF 16; which is the maximum value for a 32-bit unsigned integer in computing.

This value is the largest memory address for CPUs using a 32-bit address bus. It is therefore the maximum value for a variable declared as an unsigned integer in many programming languages running on modern computers.

Now we know why $4,294,967,295 is the limit of how much in-game cash you can earn and the significance of the number in both the fields of mathematics and computing.

Have you reached $4,294,967,295 in-game cash? Did you know the significance of the number? Are you familiar with Fermat primes? Sound off in the comments below. You know we love hearing from you.

Just hit the max! Anyone got screenshots or the dialog? I missed it as I was trying to corral a character when it hit.

Is there a maximum % bonus like there is for cash?

If there is we haven’t found it yet…

Just wow. 🥴 answered my questions and I didn’t even know I needed to ask them yet. . . . And whoa. . . . 10k % ??

🤪. Thank you!!! 😘

Took me a while to find this again but I am getting close now!

Ok. So I’m not a math guy so I don’t quite get this. I always assumed the limit would be a dollar under $10B

When I saw it went into the billions years ago I thought it would just go to the max number in single digits billions.

If it crosses 1,000,000,000 why can’t the max be 9,999,999,999? Why the 4.2B number? I know it’s something to do with it binary something or other but like I said. I’m not getting it. 10 digit numbers seems like a 10 digit numbers to my a non math brain.

Thanks in advance. Y’all are awesome.

I’m at 983,000,000,000 but have been playing since beginning

Thx for the explanation. It’s nice to know how that seemingly random number came about 🙂

Ohh this is good to know as I’m extremely close to this amount. Thanks for this post.

So we can assume player cash is stored in an 32 bit unsigned integer variable. I wonder how long in the early days that was just an overflow exception and crash? Nice that they’ve put a little story element in essentially what is an error handler.

It’ll be a long time before I hit see the max cash dialogue, but I’m not trying to do so. I’ll probably hit the 1B mark by the weekend, but as far as I’m concerned I have far more than I need. I wish I could gift extra cash and doughnuts to neighbours who could use some. 🙂

Is there any chance someone could post the dialogue for those of us who know we’re never going to have that amount of in game cash to be able to see it ourselves.

Just hit it this morning. Here is the dialogue:

Frink: Good Glavin, don’t collect another cent!

Homer. Fat chance, Poindexter. These white houses don’t farm themselves.

Frink: You fool! If you take in even one dollar more, we’ll exceed the binary dominion. You’ll destroy us all!!

Homer: Well I guess I shouldn’t do that. Again.

End message: Limit reached

Congratulations! You’ve reached the game’s currency limit! You’ll never make any more money than this, so might we suggest spending some of that hard-earned on a Sit-n-Rotate or a few thousand bloodmobiles?

I thought a billion was 1,000,000,000,000

It used to be such in the UK, but has now been adopted to mean 1,000,000,000.

I knew you’d know, just testing 😁

I love this stuff Safi, keep them coming! 👍

~MIB👤

65535 ( 2^16 -1 ) sticks in my mind from the days of 8 bit computing!

You mean 281*663D81 don’t you?🤓

SAFI MUST BE SILENCED.

Pass it on. 😋

Just don’t visit the site Monday morning Sandy Toes, lol!

I got no whete else to go!!!

Your keyboard has an occasional CapsLockStuck error😁

Haha!

I’m (ahem) “only” at somewhere over 1.3 billion… but I recently realized that my house farm (plus bonuses, plus multiplier) has reached the point where it can easily produce in-game cash faster than I can readily spend it back down. I actually had about 1.28 billion right before they released the Golden Goose; I promptly used Rat Trap Truck XP conversions to buy up somewhere over 2000 donuts in order to scarf up all of the remaining land tiles, (along with a bunch of other new offerings) and now here I am, with more currency than before.

With all of that newly obtained extra space, I had actually just removed my farm in order to more easily relocate it a bit farther from my main town area, but I was starting to contemplate whether or not to even bother putting the *entire* farm back into play, as I wasn’t sure there was really any point to accruing currency that quickly anymore. Now, you’ve given me a hint about some in-game dialog that I haven’t seen yet… so maybe I’ll go ahead and pull all 1,000 purple houses back out of storage, after all!

Not immediately, though. I think a proper redesign is a bit overdue, so I’ll probably be spending a few weeks (or months?) on that, first.

Yikes.

LOL. To which part?

My thoughts exactly.

WOW, You are hard core!!!

Nah; I’ve just been playing for a pretty long time, that’s all. The hard core players that *should* be impressing you have been playing since practically the very beginning… and run weblogs about the game. 😉

Curious. I assume your bonus % is maxed out. How much do you make in a 24 hour period Zarmanto?

I didn’t actually know that there was a “max” value for the bonus — but I do know that other people have bigger bonuses than me; mine is at about 1,300% or so, (in addition to the Springfield Heights hidden bonuses) and I’ve seen references to people with bonuses over 2K%… probably on one of Safi’s posts, but I can’t recall for certain.

As for my income in 24 hours: honestly, I stopped counting awhile ago… but in addition to the farm, I also have somewhere over 300 characters; the bonus enhances income from characters as well as from farming, so pumping up that bonus really is the key to the game, regardless of whether you do KEM farming, house farming or some other thing.

As an aside: I’ve had conversations with other players who thought I was bonkers for bothering to build such a large farm, but most of my farm was built prior to EA implementing a *huge* change to the pricing structures, when houses were a lot less expensive. It’s much more difficult to justify such large house farms today, unless you go into it with the mindset of extremely long-term planning — and frankly, this game has already lasted longer than anyone ever thought it would, so who knows how much longer we’ll be tapping? (Then again, the show is still running, too… so ya never know.)

I was curious about the maximum cash you can collect. This amount explains a lot. 32 bit programming. Unsigned integer. This brings me back to my old programming days.

I will probably never reach that point and I’m OK with that. I love these Mathematical Monday posts though! People always said you’ll never need to know these things in the real world. Yeah, well, the real world is full of nerds that DO know these things, so that argument is no longer relevant. No one is really going to be free until nerd persecution ends. Long live the nerds (and everyone that loves and appreciates everything they do to keep the world running)!!

I’d just like to point out I’m not a nerd. I’m one of the cool kids. At least that’s what my Mom says.

Mom knows best😁

I’m close. 4.1B. So after that, then what? You can’t collect more, or it just adds to the amount but you can’t see it? What happens if it dips below after you spend money on KEMs or RTTs and then hit the max again:l? Do you get the dialogue again?

And thanks for all your hard work guys.

It really won’t add up. All the income after 4.2B will be lost. You will work without any cash return.

If you do the KEMfarming or the RTT buy/sell it will be deducted from and added up.

I myself only have 1.5B

IIf EA hadn’t taken the measure, you would have lost all the hard earnings, as there no carry over.

The cash is represented by 32 bits.

The maximum amount is FFFF FFFF. Of you even earn 1 dollar the amount of cash would go to 0000 0000, which would you lost ALL of your 💰 cash 💰 There is now way to get it back😟

Wow, for once it seems someone planned ahEAd!

That would have been extremely frustrating, to reach 4.2bil, tap some houses and ACK! have no money.

~MIB👤

Hi! I took 4 years to reach 500,000,000, but now the money increase 50 millions per month (523,95% bonus). So, I will need 6 more years to reach the limit.

I think your math assumes no other changes to your income level — which is actually something that you can easily influence, if you have a mind to do so. As an example: if you wait for the Jet Engine Bike to become available in the Vault at the discounted 20 donuts price, and then focus on buying a whole bunch of those at a time in order to augment that bonus, it may not be that long before you realize that “max cash” isn’t quite as ambitious of a goal as you thought.

For me…the time involved to reach “max cash” is the deterant. I have better things to do with my time…and the “reward” being a worthless digital currency that allows me to get more worthless digital currency, seems silly. But…then again…it’s Monday, and real world goals and tasks await.

Yessss, Patric! You are right also! Well, as I am retired and only play just one game, I like to determine some goals for me to achieve, but really know that there is a limit is kind of frustant, the same as the limit of itens you can have.

A bitcoin has more value, but even that I consider it as The Dutch (Black) Tulip Mania.

https://en.m.wikipedia.org/wiki/Tulip_mania

We Dutch are so gullible 😁

“Seems silly”… I entirely concur. But it’s just a “silly little game,” as Alissa sometimes likes to say, so that seems to fit quite nicely into this context, don’cha think? And for that matter, aren’t most recreational endeavors a bit silly, in one way or another?

Take bowling, for example. (I actually quite enjoy bowling, but I’ll never be fantastic at it.) Basically, you grasp a heavy ball, whip it behind you as you run two or three steps across the floor, and throw it at high speeds down a narrow greased alleyway with enough force to slam it into a collection of wooden pins, for the sole purpose of seeing just how many of them you can knock to the floor. Kind’a silly when you really think about it, right? And yet, there are people who take bowling *very* seriously, even to the point of doing it professionally.

Or take golf… or no, maybe not. I wouldn’t want to disparage *your* favorite past-time. 😉

Honestly it doesn’t take much time at all to reach the max cash amount….assuming you are obsessed with your bonus percentage (like i was a while back). I stopped when I finally reached 10,000% bonus but once you hit 1k or so the money starts pouring in and your balance turns to a red 4g pretty darned fast.

And you might get frustrated for a second when you hit it, but then you realize the money means nothing at that point and you were only collecting for the XP anyway 🙂

These days just harvesting my town ends up generating 30 or so donuts and the only count that actually matters is the one to the right of the donuts!

Yes, Zarmanto, you are right! I only buy something with bonus when its costs less than 15 donuts/percentage. Well, I really not ina hurry to reach that goal 🙂

I never will reach it. I use the cash to grow donuts 🍩

I have specula dealership to buy and sell 🚚RTDTs🚚

special, not specula

Thanks a lot Safi! Being in the IT field, I’m familiar with the 2^32-1 number 😀 although I think I’ll never achieve this quantity of TSTO dollars!

The Euler proof is the reason I recall, after many years, that 2^32+1 equals 641*6700417.