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.
Or look at the prime pair (11,13)=(1011,1101). Each is the other read backwards.
Or take the prime pair (1049,1051)=(10000011001,10000011011). Now concatenate the binary streams to get 1000001100110000011011=2149403 which is a prime. What's the probability of that?
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 email@example.com