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 using the "left to right" convention. The first 20 primes are listed below.

For example 11=1101

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

1101 | 1011

where | donates the mirror.

11 is prime, but it's mirror reflection 1011 (13) is also prime. So 11 and 13 are mirror primes. They are also a prime pair of course.

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

Of the first 18 primes 14 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 01
3 11
5 101
7 111
11 1101
13 1011
17 10001
19 11001
23 11101
29 10111
31 11111
37 101001
41 100101
43 110101
47 111101
53 101011
59 110111
61 101111
67 1100001
71 1110001

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