# Prime magic star

Can you replace the letters with 10 consecutive primes such that the sum of numbers on each line is equal? I expect this to be solved with a computer.

Good luck!

• Is there any method to solve this besides trial and error? – Deusovi Oct 13 at 2:35
• For the record can you please stop criticizing every puzzle I post. Yes I like mathematical puzzles and some of them require a bit of trial and error. I don't see anything wrong with that. Also I think it is ok to solve puzzles with a computer. In fact there are some very clever algorithms that allow you to reduce the search space and find the solution faster. For me coding/developing such algorithms is part of the fun, especially if you can use them to solve larger cases and push the boundaries of your knowledge. – Dmitry Kamenetsky Oct 13 at 2:43
• I like mathematical puzzles too. But for something to be a puzzle, it should permit a clever "aha moment" that leads to the solution. What makes a good puzzle is a "path" to the solution, somehow "built into" the puzzle. Questions that require large amounts of trial and error don't satisfy that, in my view. – Deusovi Oct 13 at 2:45
• Your "Paint 7 cells of a 7x7 grid" had a very nice path to the solution (though I don't know whether it was intended). But I'm critical of this (and similar puzzles) because I don't think it has an "aha moment", or a natural "path" to the solution. If the intended way to solve something is brute-force search (or mostly brute-force search), I don't think it's very good as a puzzle. It may be a great programming challenge for a site such as Project Euler, but that does not make it a puzzle. – Deusovi Oct 13 at 2:51
• I agree with @Deusovi on this one, as manually solving it is practically impossible. If you intended for this to be solved with a computer, you should say so and present it as a coding challenge. As it is, one might expect to find a solution in small primes. Woe unto them. – Daniel Mathias Oct 13 at 3:04

First, this image shows examples of translation that preserves the summed groups. As mentioned in comment, there are $$12$$ equivalent arrangements in this class.

Here is a solution set:

A=13907
B=13913
C=13997
D=13999
E=13921
F=13933
G=13963
H=14009
I=13931
J=13967

There are seven other solution sets with primes less than 100,000 and countless more with larger primes.

• You got it! The first answer had a bug, but this one is correct. Feel free to post other solution sets. – Dmitry Kamenetsky Oct 13 at 21:45