#twin primes conjecture

[tanadrin]

A Magic: The Gathering combo that deals infinite damage if and only if the twin primes conjecture is true.

[markrosewater]

Mark, when will get an admission from your team that Magic The Gathering is just an attempt to draw in people to help solve long standing math problems like the twin primes conjecture?

Sssh.

[greenouillee]

Create a trading card game that requires solving an open problem to play optimally

Relate your problem to a common board game.

[clownakai]

"Dance with me."

Shuuichi very nearly chokes on his drink. "Pardon?"

Scotch smiles beatifically back at him. Definitely tipsy, at least a little bit. "Dance with me."

"I can't dance," he blurts out, the lie slipping past his lips as smooth as breathing.

Silence falls over the flat, only broken by the sound of Mochi's hissing from inside Scotch's bedroom; Hana has probably been bothering him again.

"That's fine," Scotch eventually replies, "I'll just have to guide you." With all due respect, fuck that.

"Why?"

"Well, I obviously can't let you lead if you don't know how to dance." Scotch leans back against the couch, looking for all the world like someone who just cracked the Twin Prime Conjecture or some other equally convoluted math problem (thank you, Shuukichi).

Shuuichi scowls, bringing his drink to his lips only to realize that the glass is already empty, again. "Why would I want to?" he clarifies.

"Ugh." Scotch rolls his eyes, muttering something about all workaholics being the same. "Live a little, why don't you? We can even turn the lights off if you're that embarrassed."

Way more than slightly tipsy, Shuuichi corrects his previous assessment with a sigh. "I'd be stepping on your toes the entire time if we did that."

"You'd manage it even with the lights on."

Shuuichi's eyes narrow. For the sake of his lie, he doesn't correct Scotch's claim. Let the guy believe what he wants, so that proving him wrong will be that much— hm.

He glances critically at his empty glass. He'd better cut back on the drinking for tonight, lest he want to end up embarrassing himself for real.

Then again, if he doesn't dance at all, those chances will inevitably drop to zero, thus allowing for more drinks to be had. Who knows, he might even get something mildly useful out of his flatmate in that case.

Scotch shifts in his periphery, successfully drawing Shuuichi's gaze to himself. He knows exactly what he's doing: it's in his posture, so loose and relaxed it can be nothing but studiously arranged; in his hands— long, calloused fingers loosely holding up a crystal glass (and petting Hana and chopping vegetables and dancing on bass strings and carding through Shuuichi's hair); in his eyes, so very blue and positively smoldering (there's a sliver of ice in them, ready to pierce and tear and sink: Shuuichi pretends he doesn't see it).

Tipsy, but no less dangerous because of it: Shuuichi had better keep that in mind. He should tread carefully, play it safe— turn down the offer once and for all.

Oh, who is he kidding?

"Fine." He puts his glass down with a clink. "Show me how to dance."

Scotch looks, for lack of a better descriptor, absolutely delighted. Shuuichi suddenly regrets more than a few of his life choices.

The other man stands up with remarkable grace for someone who has been drinking for the past hour and a half; he waits for Shuuichi to do the same, and at no point does he stop looking at him— through him, digging and searching and for a weightless moment Shuuichi wonders—

"I set the music up, you get the lights?" Scotch asks, blinking it all away.

Shuuichi valiantly holds back a grimace, but nonetheless moves to comply. "If we fall and break something, do me a favor and shoot me before Bourbon comes back."

Scotch snorts, and Shuuichi's stomach most definitely does not do a little victory dance. It doesn't.

He flips the light switch, plunging the living room into darkness: the only remaining light sources are Scotch's phone and a stray ray of moonlight feebly peeking past the mostly-closed curtains. Shuuichi takes advantage of those to orient himself, smoothly padding past the couch with nary a sound; he's sadly not fast enough to catch a glimpse of Scotch's screen, instead finding himself being led to the emptiest part of the room as the first notes of a simple waltz begin to fill the air.

"Right. So, the first thing you want to do is—" Shuuichi only has an inch or so on Scotch, height wise; it's certainly not enough of a difference for him to successfully pretend not to be taken by the moonlight striking the man's features, only barely reflected in his eyes.

(There they are, those shards of ice. Primed and ready, a hair's breadth away.

Ever the fool, Shuuichi inches closer.)

"— even listening to me?" Scotch asks, sounding torn between amusement and mild annoyance.

"My right hand in your left," Shuuichi absentmindedly parrots, "my left on your shoulder. You go left foot forward, the other to the right, close with the left, then right foot backwards, the other to the left, and close with the right. I just mirror you."

"... Okay, good." Scotch doesn't sound baffled, but Shuuichi is pretty sure he went a little overboard and recited something the other hadn't said yet. God fucking dammit.

"I know what a waltz is," he tries to salvage, "I've just never tried dancing it." For his own sake, Shuuichi prays that all the drinks he had tonight will help him sell the beginner act he talked himself into.

Scotch gives him no verbal answer; nonetheless, the silence feels as loud as a blaring horn to Shuuichi. Then there are hands on him, one coaxing his own upward while the other slips under his arm and comes to rest on his back, miraculously avoiding getting caught in his hair at it splays right beneath his shoulder blades, and Shuuichi almost forgets to let Scotch guide his hand into the correct position rather than doing it himself.

Right now, he might hate his own shirt more than anything.

"Alright." Scotch is... close. Not quite chest to chest, but still enough for Shuuichi to smell a hint of alcohol when he speaks. "Waltzes are in three quarters, so we're just going to— one, two, three."

Shuuichi doesn't even need to pretend: he stumbles through the first few rounds, the hand on his back burning like a brand. He wonders if Scotch can feel Shuuichi's heart jackrabbiting beneath his fingers, a caged beast in its own right.

(It sure feels to Shuuichi like it's trying to claw its way out of his chest.)

The waltz eventually gives way to a slow song Shuuichi doesn't recognize but is still aware enough to know how to adapt to: he doesn't startle when all of a sudden Scotch is everywhere, chest pressed against his and arm dipping to Shuuichi's waist and face so close the tips of their noses almost touch— yet he's deafened by his own heartbeat, a relentless drumming in his ears as Scotch meets his eyes and smiles.

"So you did lie to me," Scotch murmurs, smile widening when Shuuichi freezes. "This one's in four quarters, so it's no longer a waltz. But you didn't need me to tell you that, did you?"

Shuuichi swallows dryly. With how they're standing— with how Scotch is holding him—, the flush he can feel creeping onto his cheeks is just about the only thing he can feasibly keep to himself; everything else is fair game, from twitching hands and shallow breathing to faltering steps and a heartbeat so loud he struggles to convince himself that the other still can't hear it.

"No," he admits, and watches the ice spin in Scotch's eyes. "I didn't."

Shuuichi almost expects the operative to let go, to step back and put a healthy distance between them; what he gets is Scotch's fingers drumming a silent tune on his waist and one of the guy's legs moving forward in a tacit bid to keep dancing. Shuuichi obligingly follows, happy enough to let the other lead while he gets his shit together, although he puts his foot down the moment Scotch tries to raise their clasped hands above their heads.

"You're not turning me," he huffs, then curses himself for speaking up when Scotch's breathy laugh warms his lips.

"Next time, then." The weight around Shuuichi's waist disappears, and this time Scotch steps away for good, leaving him cold, adrift and hungry for something he can't quite place.

Shuuichi stares at his retreating form— what little he can distinguish of it in the dark, at least—, then sets out to distract himself by clearing the low table of all evidence of their drinking. It'll certainly not be enough to fool someone like Bourbon, but it'll knock 'leaving a mess for others to clean up' off the list of complaints he might receive tomorrow.

He knows what this— all of this— was. He's been taught how to do the same himself and he can't afford to fall for it.

(He thinks of those eyes, dark waters waiting to drown him.)

He really, really can't.

(Scotch took his phone with him, but Shuuichi still hears something: one-two, three-four; one-two, three-four. It's nothing like the all-encompassing drumming from before, and it makes him wonder...

Maybe his heart had felt so loud because it wasn't the only one he'd been hearing.)

[necarion]

I haven't made much progress on the twin primes conjecture recently, but I have proven that there are not infinitely many primes that differ by 1.

[bagalois]

day 17: what article or video have you seen recently that fascinated you?

so... i forgot about this challenge until i found this in my queue...

admittedly i don't have any articles or videos that have fascinated me lately. but i watched this video a long time ago, where terence tao talks about the work he did with polymath on the twin prime conjecture.

he is such a good speaker!

~~~~

day 17 of the 30 day stem study challenge

[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.

[boycritter]

donald trump has signed an executive order declaring the twin primes conjecture false

[jadagul]

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.

[anremithrl]

Lie, say Twin Prime Conjecture is true.

[foolhearteyes]

just solved the twin primes conjecture. they're infinite btw

[ghoultrifle]

Favourite theorem?

GREAT QUESTION MR BARNES

unfortunately i think my answer is a bit of a cliche. i have a soft spot for fermat's last theorem (there are no integer solutions to x^n + y^n = z^n for n>=3), not only because i have The Book on it (by simon singh, 10/10 would recommend) but because in one of my modules, we proved it for n=3 and that's so cool

honourable mention to the (not yet a theorem) twin prime conjecture because i did my diss on it. if true, then there will be infinitely many pairs of primes that differ by two. so like there are infinitely many primes, there'll be infinitely many pairs of them as well, like 3,5 or 11,13 or 39,41. idk i think that's sick

what's your favourite theorem ?

[a-lesson-you-never-asked-for]

Prime Numbers

A prime number is a number such that it has no factors except 1 and itself. These are often regarded as the building blocks of numbers, and are incredibly important from both:

a theoretical point of view, where problems such as the Riemann Hypothesis and Twin Prime conjecture revolve around the structure of primes

the application standpoint in music theory (Queen's famous song We Will Rock You has a beat that relies on prime numbers), and more relevantly, cryptography.

How do we get prime numbers

To say that a number x is a factor of another number y means that you can split y into equal groups, each group containing x things. So for example, if you wanted to divide 91 watermelons amongst your 13 friends, you can give them each 7 watermelons and everyone gets happy.

Another way of writing this is that 10 is a multiple of 2, or that 10 is divisible by 2.

With primes, you can't do this except by dividing them into groups of 1. For example, 2 is prime because you can only divide it into 2 equally sized groups. You can only divide 11 into 11 equally sized groups.

As a result, prime numbers have some very interesting properties, some of which are unknown. One very easy way to calculate them is by using the Sieve of Eratosthenes. The idea is that you start at 2 and remove every multiple of 2 except itself. So block out 4, 6, 8, 10, 12, and so on. Then you move onto the next unblocked number, which is 3. You go ahead and do the same, remove 6, 9, 12, 15, and so on. Notice that in the next step, 4 is blocked, so we go to 5, and block out 10, 15, 20, and so on. This process is very slow but it's certain. It tells you what the primes are with absolute certainty. Here's a picture to illustrate the idea. This excludes all the even numbers.

The atoms of natural numbers

Primes are regarded as the building blocks of numbers. This is due to the following theorem.

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Fundamental Theorem of Arithmetic

Any integer n can be decomposed uniquely in products of powers of primes.

Examples

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10 = 2 × 5

15 = 3 × 5

24 = 2³ × 3

There are many important theorems that come about due to primes, and almost all of them have to do with a topic called modular arithmetic.

Where to from here...

This is probably the extent to which you need to know about primes. Most of the ideas used will be introduced, as mentioned before, on an ad hoc basis. We will focus more on the code building aspects in our next parts, talking about binary and ISBN codes, before moving onto some more complicated examples of encrypting information.

[markrosewater]

On behalf of Mel/J*nny math nerds, high-fives to the designers who made it possible to build Turing-complete decks, NP-hard blocking legality decisions that make Sparky get it wrong, and now a Zimone deck that can deal infinite damage only if the Twin-Prime Conjecture is true!

High fives shall be delivered.

[topoillogical]

One of my funner opinions is that one should try to solve any unsolved math problem that calls to them. I think it's good for the soul

Try and figure out where to start! How would one even go about proving twin primes? Or, just pick a place and start there. Say "suppose there are finitely many mersenne primes, and let M be the largest". What does that imply? Suppose there is a cycle in the Collatz conjecture. Can you say anything about it? No? Why?

Just like... let yourself think about it and poke at it and you'll get a better understanding of why it's so hard, and maybe learn something new, and maybe have a good time

[nerdlycrying]

ok so what have i been up to for the past month of silence?

*deep breath*

there is a way to, consistently, find the next prime number in a list of them. the only problem is the proof for the equation relies on the twin prime conjecture being true. oh and the proof is several pages long outside of that. and this sequence goes negative, in a way that isnt just "-2, -3, -5, -7,...". The sequence of negative primes is as follows: "-3,-5,-7.777 repeating,-7,-8.888888887823948 repeating, -9,...". negative primes are quite an interesting phenomenon, and the equation to get them is definetley not anywhere near a standard equation. it involves relying on signs of numbers being set values, indexes of seemingly random prime numbers, and of course only works in base 1221.

so thats what ive been doing. tl:dr: nerdy math shit