20220105, 17:50  #1 
Aug 2002
2^{2}·2,129 Posts 
January 2022

20220107, 05:04  #2 
"Max"
Jun 2016
Toronto
2^{5}×29 Posts 
Min/max for 7/5 case? 446/3051?

20220107, 18:29  #3 
Jan 2021
2·3 Posts 
I can confirm those numbers...
/Thomas Egense 
20220107, 18:53  #4 
"Max"
Jun 2016
Toronto
2^{5}×29 Posts 
Thank you! I sent my 7/5 solution yesterday.
What did you code in? What was the total runtime? I coded in Python, it took ~24 minutes to solve the n = 7, d = 5 case. Java should be faster for sure. Is anybody working on n = 8, d = 6? It would be nice to see the min/max counts (please don't post the solutions, just the counts). 
20220107, 19:01  #5  
Jan 2021
2·3 Posts 
Quote:
It took about 2 minutes to solve in java for n=7,d=5. I did not really optimize except first generating cache of small primes. The n=8, d=6 was solved in some hours, did not time it. For n=8, d=6: wheeel for maximum solution had 1992 primes wheel for minimum solution had 741 primes. 

20220107, 22:00  #6  
"Max"
Jun 2016
Toronto
2^{5}×29 Posts 
Quote:
Thank you! 

20220109, 21:46  #7 
"Walter S. Gisler"
Sep 2020
Switzerland
15_{10} Posts 
I can confirm the scores for n = 7 and d = 5.
For n = 8 and d = 6, I get the following scores: max: 19690 min: 6905 Average execution time (using Cython, and only one thread  could be easily parallelized): n = 7, d = 5: ~120 seconds n = 8, d = 6: ~1100 seconds 
20220109, 22:35  #8 
Sep 2017
207_{8} Posts 
I have a circle with score 21617 but my min is not even close to yours.

20220110, 04:24  #9 
"Max"
Jun 2016
Toronto
2^{5}·29 Posts 
> but my min is not even close to yours.
It might be that the problem got edited after the initial posting. The first sentence reads: "Seven distinct digits are placed on a circle." (also, "placed" is misspelled in the original) I had much lower min scores (60 instead of 446) when the circle of 7 was allowed to have duplicates. No duplicates allowed, neither in the circle, nor in the numbers. Thank you for posting your scores and times! 
20220110, 04:49  #10 
Sep 2017
3^{3}·5 Posts 
I meant my minimum is much higher. I do hope someone who solved the bonus can post their scores for min and max.

20220110, 05:38  #11 
"Walter S. Gisler"
Sep 2020
Switzerland
3×5 Posts 
Just to add on to my previous response: the number of primes that can be generated with the max and min wheel in my solution corresponds to the same values that Zoozie posted (741 primes for the min wheel and 1992 primes for the max wheel). Now, to be fair, I see multiple wheels that generate the same number of primes, but it gives me some additional confidence that my solution is right.

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