Primes Within Primes

Primes Within Primes

If you write a prime number in binary you can sometimes split it into 2 segments each beginning and ending with 1 that are also primes.

For example, the prime number 7591 is 1110110100111 in binary. Now snip out the first segment 11101 which is 29 and prime. Then snip out the second 10100111 which is 167 and prime.

So, denoting a binary string concatenation operator by "+" we can say 7591=29+167

Notice that our concatenation operator depends on order, so n+m is not the same as m+n. Mathematicians call this kind of operator "non-commutative".

Let's do a simple example with our new operator..

In binary 3 is 11 and 5 is 101 so 3+5=11101 which is 29.

But 5+3=10111 which is 23.

By the way, notice that all these numbers 3, 5, 23, 29 are prime!

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Content written and posted by Ken Abbott