Making Prime Numbers - A Conjecture

Making Prime Numbers - A Conjecture

Take any prime number. You are allowed to insert a single digit (i.e. 0-9) anywhere in the number, including the beginning and end (but we don't count adding a 0 at the beginning of the number because that just gives the original number.)

Conjecture: This process will always generate at least one new prime number.

Doing this in binary (base 2) means the only digits I can insert are 0 and 1 and it makes the process very simple. The conjecture of course remains the same.

If you write a program to test this conjecture I would love to hear about your results.

Examples in base 10
503 is prime. I decide to insert 2 before the 3 to get 5023, which is prime.
20129 is prime. I decide to insert 5 at the beginning to get 520129, which is prime.

Example in binary
Take the number 3 in binary (11), so the process generates 3 new numbers..


And in this case it has generated two new primes, 5 and 7.

Content written and posted by Ken Abbott