20230315, 17:41  #23 
Sep 2017
5×41 Posts 
Can you add a zero to the left at any point (only to be able to add another digit later)?

20230315, 17:51  #24  
"Ed Hall"
Dec 2009
Adirondack Mtns
3·7·263 Posts 
Quote:


20230315, 18:16  #25 
Jan 2017
163 Posts 
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.

20230315, 20:23  #26  
Sep 2017
5×41 Posts 
Quote:


20230315, 23:54  #27 
"Ed Hall"
Dec 2009
Adirondack Mtns
3·7·263 Posts 
Sorry if my last post seemed rude. Thanks for all the assistance, everyone.

20230316, 05:48  #28 
Sep 2017
5·41 Posts 

20230316, 12:00  #29 
Just call me Henry
"David"
Sep 2007
Liverpool (GMT/BST)
2^{2}·3·7·73 Posts 
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. 
20230316, 13:52  #30  
"Ed Hall"
Dec 2009
Adirondack Mtns
3×7×263 Posts 
Quote:
Quote:


20230316, 17:39  #31 
"Kebbaj Reda"
May 2018
Casablanca, Morocco
2×53 Posts 
very nice question
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. Last fiddled with by Kebbaj on 20230316 at 17:44 
20230326, 10:12  #32 
"Kebbaj Reda"
May 2018
Casablanca, Morocco
1101010_{2} Posts 
Finally, I was able to have it this morning. It was not easy! The football match: Morocco  Brazil (21), gave me motivation yesterday.
This morning my little laptop 8yearold 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 Last fiddled with by Kebbaj on 20230326 at 10:13 
20230403, 08:56  #33 
Just call me Henry
"David"
Sep 2007
Liverpool (GMT/BST)
2^{2}×3×7×73 Posts 
Was a there a better solution for this challenge than recursion exiting after too many exceptions?

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