Brainsteem Compute #3 Prize Computational Maths Puzzle [Win 40% and 10% in SBD]

Problem #3 is slightly different in that it is more of a research project, perhaps even a collaborative effort. The reason for this is that I'm proposing a question to which I don't know the answer!

We expect a quizmaster to know everything, but a research proposal? Well, it could be brilliant, it might be inconclusive or it might be impossible to compute. So let's find out.

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The Background

Firstly, you must read Brainsteem Compute #2 as it has all the background to this question. The standard literature talks about left-truncatable and right-truncatable prime numbers.

I prefer the term nested primes as, in this case, we are going to look at mixing the two algorithms together. It is also easier to think of this as building up the prime from a single digit, rather than step-wise truncating the final answer down to the starting prime.

The Question

Find the largest possible prime number that can be generated by starting with a single-digit prime and adding digits to either the RIGHT or to the LEFT of each prime, so that each number in the sequence is a prime number.

We shall exclude zeros, so that we cannot have the sequence: (3, 13, 013, 1013, ...) One example of the start of a sequence is: (3, 13, 137, 2137, 62137, ...)

For the First Prize, please include a valid method, algorithm or post the code and output. If this sequence is infinite, then try to prove that it is so.

If two different people get each of A and B correct, I shall split the First Prize. All others can participate so long as you have done or attempted either A or B.

Remember that even if you are not the first to post, this remains a learning experience that can help in future Brainsteem challenges.

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Prizes

To qualify you must upvote this post and write the answer in a comment.

To win First Prize you must include the answer and a valid method.

The First Prize will be 40% of the earnings generated by this post, paid in SBD.

The Second Prize will be 10% of the earnings generated by this post, awarded to any other correct answer in the comments section, chosen at random and paid in SBD.

Also remember that your upvote generates curation rewards for you and that 25% of all earnings are given to upvoters.

Prizes will be awarded after the 7 days have expired. Winners will be announced in the comments below after the draw.

The Prizes will increase with more participation and as the earnings increase.

The main thing is to enjoy the challenge and maybe learn something new.

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