### Back with a math puzzle after a bit of a blogging break

It’s been too long. Here’s a short puzzle I saw that I thought was interesting:

How many prime numbers are there that start with a 1, alternate 1’s and 0’s, and end with a 1? Of course you should explain your answer…

The problem was originally stated in based 10, but I thought with a bunch of computer geeks in the audience, I’d ask about base 10 as well as binary and hexadecimal.

Have fun,

— Max

1. David on

Interesting question. I’m going to go out on a limb here, but I know the answer to this. Somewhere between 0 and infinite. Hope someone has an answer.

2. Carter Shanklin on

I assume you don’t mean random choice but just an alternating sequence of 0 and 1, then only 1 and 101.

There is probably a cleaner answer but
10101 = 11100 – 999 = 111 * 100 – 111 * 9 = 111 * 99
1010101 = 10001 * 100 + 10001 = 10001 * 101
101010101 = 11111 * 10000 – 11111 * 909 = 11111 * 9091
and these two patterns repeat.

3. Max Schireson on

Nicely done.

4. fibonicci on

Yes i agree with Carter Shanklin