#Twin primes

[3-slugcat-pilots-7-ornithopters]

Okay so this is taken from the Three Card Blind discord server from an acquaintance of mine, Quag.

It’s Alice’s turn and she controls Zimone and has a Fling, an Awaken the Woods, and a fragmentize in hand. She controls 2 Forests (green mana), a Plains (white mana), a mountain (red mana), as well as two lands that are here because they can be sacrificed.

Both Alice and Bob have infinite mana colorless mana made via an artifact that can untap itself for more mana.

Bob has 10 life and controls a Wasteland and two Forests. He has a Nourishing Shoal in hand. He also controls a Battle of Wits and has 250 cards in his library.

To win before Bob does next turn, Alice needs to create a large creature token with Zimone by casting Awaken the Woods, and at end step Fling the token. However, Bob with his infinite mana can cast an arbitrarily large Nourishing Shoal, gaining 10^100 life for example. Alice will try to Fragmentize the Monolith that Bob controls. In response he will generate the mana to cast the giant Shoal and he has to pick a number.

Then, Alice can cast Awaken the Woods to make her land count a prime number that is bigger than 10^100 so that at end of turn, she can Fling the Primo token at Bob’s face. However, once the trigger goes on the stack to make the token, Bob can Wasteland any of Alice’s non basic lands to make her total land count a composite number, making no token.

But, Alice has a trick! She can sacrifice one of her own Havenwood Battle grounds to make her number of lands 2 less in combination with a wasteland. This would allow her to still have a prime number if she chose the larger of a pair of twin primes as her target land count.

The question is this: Can Alice always make a number of lands bigger than any other number so that if Bob destroys one of her lands, she can sacrifice another, remaining at a prime number, and making the token to Fling for the win?

(So: are there infinite twin primes?)

Did you see that Magic: the Gathering now has a game state in which you need to prove that there are an infinite number of twin primes to win? I can explain it more if you are interested.

(With reference to this post here.)

By all means, please tell us about the Magic: the Gathering combo which requires proving the twin prime conjecture in order to win.

[chaotixcx]

Give those guys some Sanrio plushies!!!!

[crispy-art-on-fire]

Shockdad dealing with 50 years of not seeing his son very well and totally normal.

I am enamored by the idea of Longarm Prime just being a little bit of a freak. His fake face gathers all the tears behind it and so it spills out of his mouth like drool or vomit instead of his eyes.

[pastelpaperplanes]

I am not biased. why would you say that to me.

[xanthumn]

from The Solitude of Prime Numbers by Paolo Giordano, 2008

this excerpt means everything to me you don’t understand

[ailithnight]

DPxDC prompt #15

Demon Twins Fic

But!

Okay, so something I've seen floated a time or 2 from DC is that when using the Lazarus Pits to revive, a person emerges completely healed of all previous injuries or illnesses. Including scars.

Now obviously fandom often plays fast and loose with this rule, given how we like to give Jason an autopsy scar and some folks also like to make him keep the J from the Joker. But let's lean into it a bit here and make it play nice with the DP side of things.

Let's say that it's the ectoplasm, even the rancid stuff in the pits, that heals all scars except Death Scars.

So if Danny was, say, revived in the Pits by Talia before she disappeared him away to an orphanage in Illinois? The Danny that shows up in Amity Park wouldn't be covered in scars from his time in the League. He'd only have the one, the Death Scar.

Similarly, the Danny that stumbles out of the portal wouldn't have any scars from his time in Amity Park. He'd only have 2, the original Death Scar and the new Lichtenberg Death Scars.

Now I've seen it done many times where the Bats/Damian realize that Danny isn't a clone because you can't clone scars. So if Danny doesn't have those scars, and if his DNA is too messed up from the ectoplasm in him to check for any "regular cloning markers"...

Danny, fresh from an autopsy table, runs to Gotham to hide. And because of his inability to walk away from someone in danger, gets found by the Bats. Whether or not they know about Damian's twin beforehand, they are quite confident that Danny is a clone. An exceptionally good clone with nearly perfect implanted memories, but a clone nonetheless. Damian is particularly enraged about this

And poor Danny, already all sorts of fucked up from growing up Damian's lesser, then Dash's punching bag, then an experiment; in the face of Bat certainty and lacking any tangible evidence to the contrary; Danny starts to believe them.

[cynosurus]

Gusu Lan has Wangji and Xichen, the Twin Jades,

Yunmeng Jiang has Wei Wuxian and Jiang Cheng, the Twin Heroes,

but actually, this year me and MY brother are also the Twin Primes of our family!*

*In that our ages are twin primes, prime numbers that are only one number apart.

[suna-gab]

Uh-uh Someone didn’t behave☝️

Better be honest, kids.

Prowl knows

[12neonlit-stage]

Some kid icarus doodles cuz I got fixated on Pit... ft. extra doodle of pit hugging Pittoo cuz they the twins ever

[farouche-landau]

How would the Turing machine know that it's run out of twin primes? It seems like that would require an infinite amount of computation. Interestingly, this wouldn't be a problem with the Goldbach conjecture, which if it's false can be disproved by finding a number that isn't the sum of two primes. (If I were a logician I would know the name for the distinction between these two types of statements, but I'm not.)

You could make a Turing machine that looks for a proof of the Twin prime conjecture (in your favorite axiom system), giving you a game where Alice wins if and only if the Twin Prime Conjecture is provable. (Or of course you could do the same thing with a disproof.) But I think it's not entirely implausible for the Twin Prime Conjecture to be independent of ZFC, so "the Twin Prime Conjecture is provable" is not the same thing as "the Twin Prime Conjecture is true".

Which was one of my quibbles with some of the original descriptions of the twin primes combo: Alice doesn't need to prove the twin prime conjecture to win, just as long as there are infinitely many twin primes she's guaranteed to win. (This ignores the computational complexity issue where Bob can name a number so absurdly long that Alice can't find the twin primes after it before the heat death of the universe. But I think the computational complexity version of this game actually works in Alice's favor, because she just needs to find numbers that Bob can't factor.)

Since you're posting on the twin primes MTG combo: am I correct in thinking it was already possible to create a game state where the winner depended on whether the twin primes conjecture is true, due to the fact that you can establish a Turing machine in MTG? (Zimone, All Questioning just makes it simpler to do this, at the cost of making the relevance of the twin primes conjecture come in via game theory rather than just via resolving the rules.)

That does seem to be the case. Having now skimmed the paper, that's a much stronger result, because neither player ever has any choices to make. If you feed it a Turing machine that halts when it runs out of twin primes, which I think you can construct, then Alice wins if the Twin Prime conjecture is false and the game draws if the Twin Prime conjecture is true.

[umaia3aurart]

Practice drawing twins!

[snailsfall]

[rizzem-w-the-tism]

Why was he lowkey a diva

[farouche-landau]

I mentioned this briefly in my other post, but I think (having played maybe 4 games of MtG in my life and knowing nothing about tournament play) that any realistic version of this game favors Alice, because she doesn't actually have to come up with primes, she just has to come up with numbers that Bob can't factor.

So say, if Bob says "one million", she could say "one million factorial plus one", and then Bob would have to factor one of (10^6)!+1 or (10^6)!-1 to block her. (Hopefully some clever person who knows number theory will say "but what about Wilson's theorem?" But it doesn't help here because 10^6+1 is easily checked to be composite, so doesn't divide (10^6)!+1.)

Ok first of all, the MTG game state doesn't just need the TPC to be true, it also needs a way to generate arbitrarily large twin primes, which I seriously doubt will ever happen. I'm not sure I understand your objection but Alice can't simply pick a larger prime number than Bob's number: He can respond (once) by reducing her number by 1, making it composite and her card doesn't work if it's composite. She can however, reduce her number by 1 also, making it prime again/the smaller twin prime.

My objection is that in a game, it sounds as if the players need to designate specific numbers. I'm no mathematician, but I don't think finding out whether a specific number is still prime when you do stuff to it proves stuff about all numbers.

[raileurta]

If Cody, Miko, the twins, and Shockwave were locked in a room together they would probably make a black hole by accident and or figure out a way to kill god.

[fadeintoyou1993]

i'm still trapped inside that mirror, where i painted my eyes gold, among the last remaining pride my adolescence used to hold

lyric & poem — "lonely is the muse" by halsey / @tiredandlonelymuse