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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.

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

Example in binary
Take the number 3 in binary 11=3.

If I insert a 1 at the beginning (or in the middle, or at the end) I get 111=7 which is prime.
If I insert a 0 in the middle I get 101=5 which is prime.

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

Content written and posted by Ken Abbott