Let f:Z->Q be a bijection such that f(0)=0 and f(1) = 1. Let g:Q->Z be the inverse of f.
Define a binary operator +' such that for a,b in Z,
> a+'b = g(f(a)+f(b))
where + represents the typical addition operator on Q. Similarly, define *' such that for a,b in Z,
> a*'b = g(f(a)*f(b))
where * represents the typical multiplication operator on Q. It is trivial to show that {Z, +', *'} is a commutative ring and that its additive and multiplicative identities are 0 and 1 respectively.
Let p in Z be given such that p is nonzero and non-1 and suppose that for some a,b in Z, there exists an x in Z such that > p*'x = a*'b
That is, p|(a*'b) in {Z, +', *'}. Define the integer z = g(f(b)/f(p)) where / represents the division operation on Q. Because p is nonzero, z is well defined. Observe that > p*'z = g(f(p)*f(b)/f(p)) = b
Therefore, p is a prime element of the ring {Z, +', *'}. Therefore the set of prime elements of {Z, +', *'} is identical to the set of solutions to the equation >n≠0,1
for n in Z. Thus, n≠0,1 is our prime-generating formula.
Hi all--I am trying to understand array formulas better and came across a prime number tester that I don't understand. This may be a math question wrapped in an excel question, but I'm not sure. Can anyone help me understand why this formula uses ROW()? In addition, separately, I've seen MOD() use ROW() before but have never understood why that was necessary. It doesn't work without it, but I don't know why.
I'd appreciate any thoughts you have!
This is the formula I found via google and haven't been able to understand:
>=IF(A2=2,"Prime",IF(AND(MOD(A2,ROW(INDIRECT("2:"&ROUNDUP(SQRT(A2),0))))<>0),"Prime","Not Prime"))
In playing with it, I can see that:
- it uses the SQRT() to set an efficient limit on the number of digits it will check;
- INDIRECT() appears to be used to provide a list of digits; and
- IF(MOD()) is used to see if the number being checked evenly divides into the integers between 2 and an efficient stopping point;
Just for fun, I'm also looking for alternative ways to check for primes that aren't VBA. I can't think of a way to do it without an array formula or a massive number of helper columns, but would love to know if anyone can think of another way.
Thanks!
Growing and building our armor from nothing into legendary (or even exotic!) armor with general or activity-specific set perks would be a fantastic approach.
They're on the right track. Combine these two concepts (maybe even for weapons, too!) and I think we'll see a really great evolution of Destiny's items and reward structure.
For instance, perhaps the formula could be something like 3^n , which would mean that for the nth prime number, it is always the case that it will be less than 3^n . It wouldn't even have to be the tightest upper bound (although, that would be ideal), but I'm just curious if it's at all possible to prove an upper bound for the nth prime.
Being able to prove that the highest power of 7 contained in 10000! factorial is 7^(1665) on paper is amazing. Besides proving Kummer's theorem, does Legendre's formula have any use cases in science?
My close friend has done a fantastic video discussing the upcoming MP4 and things he’d like to see, it’s started a great discussion in the comments section and I’d love to hear what you guys want to see in MP4 and how you’d like to see the game evolve.
Would you like to see multiplayer in some form or another? Maybe a change to the upgrade system? How about a physics engine similar to BoTw, whilst still keeping that metroidvania progression style?
Would love to hear al your thoughts.
Edit* forgot to include a link to video -
https://youtu.be/4GFOOCbW45s
Amazon.com has Prime Day deals on Enfamil (not sure about other brands). Their "combo packs" of 115-125 dry ounces (a mix of tubs and refill packs) have a 35% off coupon on them, and it works on the subscribe and save (5-15% off, depending on your number of subscriptions). I grabbed 118.1 dry ounces of Enfamil Gentlease for $75!!
CaCl
Then is the formula for ice H20 cubed?
It said "NO"
I'm excited to share with this community that my 15 min short film is on Amazon Prime now for free if you are a Prime member. I wrote it, acted in it and produced it. It's my first film with a budget and the director and myself went out and made it ourselves.
'Alien Guy Tim' is a mockumentary that follows an outcast who sets out to prove that he has been abducted by aliens but he faces many obstacles along the way. UK Film Review called the film "a bit of the kooky good stuff," and I hope you feel the same way about it too.
Here is the film: https://www.amazon.com/Alien-Guy-Tim-Patrick-McElroy/dp/B08NN7YQJZ
And here is the script:
https://drive.google.com/file/d/1pkAdzSW1PkDHXo4V6OzhRMplrBRBhVLi/view?usp=sharing
I would be happy to answer any questions you have about the script or the film itself. I'd also take any constructive feedback you have about it. I'm working on a second draft of the feature version now, and we are hopeful that one day we will be able to make a full feature based on the short.
Thanks for taking the time to check it out!
Context: I have a workbook of people's names with randomly assigned numbers ranked from 1-100. Based on those assigned numbers I want to autofill my attached table with the associated name.
Example: [Name] |1|51|72|14|33
The formula would then fill in squares 1, 14, 33, 51, 72 with [Name].
Any ideas?
Edit: Excel Version 2012
https://preview.redd.it/pdtk6yyagdd61.png?width=1408&format=png&auto=webp&s=31baa5e198b6ccba1b907e79862ebf893d891d5d
I recently started working as a cashier at a grocery store and occasionally we get a parent who needs the manager to grab the formula. We keep it under lock and key up front. Apparently people were stealing it.
I’ve checked out a couple people who bought formula before and didn’t bother checking the price because let’s face it, I don’t care and you’ve already spent $200+ in groceries that I have to bag so I don’t have time to check a price.
Well today I looked. This guy bought two formulas for $39.99(US dollars)EACH. His small grocery shop suddenly went above and beyond $100 and he barely had any food. I couldn’t stop myself from saying “Jesus! I’m never having kids” really loud and both the man buying it and the customer behind him laughed. Ngl I expected to hear the older lady tell me something like “oh but they’re cute so it’s fine” but instead she said “I couldn’t WAIT for my kid to turn old enough to stop needing formula.”
And now I no longer feel bad about spending $50 on books the other day. Want to know why? Because I don’t need to buy $39.99 formula for a potato
