**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