Mirror Primes

Mirror Primes

A formula that generates the prime number sequence is the "holy grail" of mathematics. It's never been found.

But here's a bit of fun..

Write a prime number in binary notation. The first 20 primes are listed below.

For example 11=1011

Now reflect 11 in a mirror on the x-axis thus..

1011 | 1101

where | donates the mirror.

11 is prime, but its mirror reflection 1101 (13) is also prime. So 11 and 13 are mirror primes. They are also a prime pair.

Some primes are their own mirror, for example 5 is its own mirror, and so is 7.

Of the first 10 primes 8 are mirror primes!

But a word of caution. Be very careful about thinking you've found a property that applies to all primes just because it works for some examples you test.

2 10
3 11
5 101
7 111
11 1011
13 1101
17 10001
19 10011
23 10111
29 11101
31 11111
37 100101
41 101001
43 101011
47 101111
53 110101
59 111011
61 111101
67 1000011
71 1000111

Content written and posted by Ken Abbott abbottsystems@gmail.com