… an infinite number of primes that differ by 2.
++++
Well they have to be odd so they can’t differ by 1. The same argument says they can’t differ by 3. Clearly that applies to 5, 7, 9, 11 … as well.
But there are a lot of primes. An infinite number I believe. So differing by 2 would seem to be relatively common at least as primes go. Seems likely there are an infinite number of them.
My more simple “proof”. 😎
Correct, there are an infinite number of primes.
If there were a finite set of primes, one could multiply all of them, and add one to the product. The result would not be divisible by any of these primes, so it would be a new prime.
… an infinite number of primes that differ by 2.
Yeah, I was going to ask if these pairs qualify:
1 and 3
3 and 5
5 and 7
and infinity is really, really big, and has lots of pairs.
PS I don’t think 9 is prime.