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Generating Primes from Primes

Generating Primes from Primes

There are many ways of generating primes from primes.

Take 3=11 in binary. It has a sequence of 2 adjacent 1's so simply insert a 0 between them to get 101=5 and prime.

Or take 7=111 here we have two ways to insert a 0, one is 1011=11 and prime, the other way is 1101=13 and prime. And in this case we actually generate a prime pair!!!

Of course, this simple method does not always work.

Here's another interesting observation..

Again in binary. 11 is prime, 111 is prime, 11111 is prime, 1111111 is prime. Notice any pattern here?

But alas, as with all "prime patterns", they work for a while and then fail. Primes are truly unpredictable. But it's still fun looking for patterns. Maybe one day!

Content written and posted by Ken Abbott