What are Twin Primes?

Twin Primes are pairs of primes whose difference is 2. The Twin Prime Conjecture posits that there are infinitely many of them, but nobody has proven it yet. Here, I dodge that question and instead show a Cute Little Fun Fact about Twin Primes.

[ihsansvlogs]

Broooo I finally found the perfect video after an hour of searching

[metaplayzfn]

Nice clarified my doubt very well, thank you!

[bobbun]

You can do slightly better than saying prime pairs sandwich a multiple of six. The table in the video is a simple expression of the idea of wheel factorization (there's a Wikipedia page, just like for sexy primes!). The next larger table would have thirty columns, and an examination of those columns would eliminate one of every five multiples of six as a candidate, because one of the columns would have no possible primes past some lower bound. After that, you could build a table with 210 columns and eliminate another class of multiples of six as sandwiched values, etc.

An observation about this idea, though, is that it really doesn't really narrow down prime pairs so much as it just narrows down primes. As should be obvious from the six table, it's not actually prime pairs that are excluded--it's primes that are excluded and the exclusion of prime pairs just sort of comes along for the ride.