Ponder This - March 2023

[SmartMersenne]

Can you add a zero to the left at any point (only to be able to add another digit later)?

[EdH]

Originally Posted by uau

First, the description defines "n-exception chained primes" as numbers appearing in a chain with at most n exceptions (so any number in a such a chain satisfies the definition). Then it explicitly confirms that with "Note that p can also be non-prime, if it is considered one of the exceptions.".

Earlier there was also a remark in parentheses something like "so it'd be called a non-prime n-exception chained prime?", making that part even harder to miss, but that extra remark has apparently just been removed.

OK, I give up.

[uau]

Originally Posted by SmartMersenne

Can you add a zero to the left at any point (only to be able to add another digit later)?

No. While that is perhaps not quite 100% clear from the description, allowing it would render the question meaningless. If you start with a prime, then adding zeros to the left would keep it a prime, and if you test enough zero prefix lengths, eventually you're expected to find one such that you can add another digit to the start while keeping it a prime (1000000000000000000000000000000000000003 and so on). This would allow you to get arbitrarily high numbers even with zero exceptions.

[SmartMersenne]

Originally Posted by uau

No. While that is perhaps not quite 100% clear from the description, allowing it would render the question meaningless. If you start with a prime, then adding zeros to the left would keep it a prime, and if you test enough zero prefix lengths, eventually you're expected to find one such that you can add another digit to the start while keeping it a prime (1000000000000000000000000000000000000003 and so on). This would allow you to get arbitrarily high numbers even with zero exceptions.

Good point!

[EdH]

Sorry if my last post seemed rude. Thanks for all the assistance, everyone.

[SmartMersenne]

Originally Posted by EdH

Sorry if my last post seemed rude. Thanks for all the assistance, everyone.

I don't think it was rude, but you gave up easily. It is really not that hard to understand: the last number of the sequence may or may not be a prime itself, that's it.

[henryzz]

Although my code doesn't assume that the last one is prime my final solution was prime. Is anyone who has solved willing to check my solution by PM? They are quite slow at confirming results are correct.

I think I have a bug in my code that undercounts the number of exceptions by 1. If undercounting(or more likely applying the cutoff) is the only issue then I have the largest solution for 6 exceptions as well as 5.

[EdH]

Originally Posted by SmartMersenne

I don't think it was rude, but you gave up easily. It is really not that hard to understand: the last number of the sequence may or may not be a prime itself, that's it.

The problem is that I haven't done any of these puzzles for a long time because I couldn't understand what was asked for. I "thought" I could do this one, but if I still don't understand this simple a puzzle, then I should give it up.

Originally Posted by henryzz

Although my code doesn't assume that the last one is prime my final solution was prime. Is anyone who has solved willing to check my solution by PM? They are quite slow at confirming results are correct.

I think I have a bug in my code that undercounts the number of exceptions by 1. If undercounting(or more likely applying the cutoff) is the only issue then I have the largest solution for 6 exceptions as well as 5.

I don't think my code assumes prime for the last one, either, but not because I took that into consideration in my programming. I also wrote a small bash script which uses gp to check the number of exceptions for the result.

[Kebbaj]

I haven't participated in a long time.
when I saw this very nice question I could not resist.
I try a code quickly, and i found a number at 23.

[Kebbaj]

Finally, I was able to have it this morning. It was not easy! The football match: Morocco - Brazil (2-1), gave me motivation yesterday.

This morning my little laptop 8-year-old with and 8go RAM was able to give me the results of all possible cases.
The last chance with the last code inspired. Ran at midnight. Best result is 28 Digits.

A lot of test with a result always of 26 digits, I was even going to give up. Now I even have a 27 Digit solution.

to soccer!!! And the Moroccoan team football who inspired me.
Thanks to the web master for this beautiful Challenge

[henryzz]

Was a there a better solution for this challenge than recursion exiting after too many exceptions?