MPMP: Prime Pairs Puzzle

Submit your solution to the Prime Pairs Puzzle now! You have one week.

All the details for Matt Parker's Maths Puzzles can be found on the Think Maths website.

Thanks as always to Deanna Judd, Zoe Griffiths and Oliver Dunk for their help running MPMP.

CORRECTIONS
- None yet, let me know if you spot any mistakes!
- But I should say: sorry that the sound 'clips' a lot in this video. I didn't notice my mic input was too loud when I recorded the video. And you only get one take for MPMP videos. You heard me. ONE TAKE.

Support my channel and I can make more maths videos:

Filming and editing by Matt Parker

MATT PARKER: Stand-up Mathematician

[Lynixai]

Thank you Matt!

First one I've attempted myself, used the playing card method and it was good fun to figure out. Might have a go at seeing if I can find other solutions since I got it first try.

[TheKingOfToast]

This one definitely seems fun to try and it's doable in the way I like: scribbling on scrap paper.

[mrtnsnp]

This was one where doing it manually is actually faster than writing the code.

[jonathanlevy]

cant wait to find all of those hamiltonian paths...

[priscillah]

I woke up early before my alarm for work, saw this video, watched it, and thought, "That's one I could give a go!" I've never done one of these puzzles before. I think I got it too :)

[thebestnerd]

1:56
there are 17536 solutions for 12

[Double-Negative]

1 2 3 4 5 6 7 8 9 is extremely close to a solution

[PronteCo]

To clarify, are we just saying that the sum of any two consecutive elements is prime?

because I am getting 17536 solutions for [1...12], which is a bit more than 2

[AugustMcKenna]

4 solutions found in less than 30 minutes! Great puzzle!

[t]

Sill waiting for the solution video. It's already past midnight in the UK.

[filipsperl]

Alright, I've just finished coding my 3rd MPMP Python script. I'm starting to learn. This one only took the entire day, but just because I made a second, memory friendly version that doesn't take too long for sequences up to 16. I'm kind of proud :)

[madisonmaley]

I stumbled into a solution on my first go thru on this problem. Very happy!

[alexanderkonczal]

Only one I've been able to do in my head; nice to have an accessible one in there once in a while. Thanks!

[senavarr]

This challenge was probably the one I've beaten the fastest, and also one of the most fun. I started in Excel, then switched to pen and paper to do some scribbles, found the answer, then went back to my computer to sketch some designs expanding on the solution, and ended up scribbling once more.

[elygolden]

Fun fact: Just like in the squares problem, one can construct a graph where the vertices are {1, .., n} and they are connected iff their sum is a prime. 9 is in fact the smallest value for which this graph is nonplanar, and this graph is nonplanar for all n > 9

[leefisher]

Note that there can't be a cyclical solution for this, because (not really a spoiler) you have to arrange the numbers Odd, Even, Odd, Even, Odd, Even, Odd, Even, Odd; and cycling this around gives you Odd+Odd which is going to be divisible by 2.
I have no idea whether either of the solutions going from 1 to 12 works cyclically, or even if it's something Matt mentions later in the video (I paused to give my solution and then make this comment at 2:18) but it might be something to mull over later when I have more mulling time. At the moment, I don't.

[andrewf]

This is if you pick any ADJACENT pair, not if you pick any pair.

[LVo]

Oh hey, it seems this time there's a whole Solved-It-During-The-Video gang! :D

[FlorianLinscheid]

I you've seen the numberphile video you know the deal how to do that. Not that you need much working out there, but we learned the right tool to tackle this thing systematically.

[Vares]

Got it. I liked your suggestion of using playing cards, made it much easier.