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Prime Place Puzzle Query

Just wanted to clarify
in this puzzle inverse diagonal rules is applicable right ?
if no diagonal means sum should not be prime ?
Thank you

Yes, your assumption is correct. If the diagonal is not marked, the sum is not prime. If the diagonal is marked, the sum is prime.

(Also, please note that 1 is not prime.)

What does "adjacent" mean in this puzzle? Only the two cells that touch by corner? Or the whole group of cells that have common diagonal line? What about situation where three neighbouring cells (by corner) have common diagonal line? Do we consider the sum of all three numbers or may we divide them into two pairs? For example cells with numbers 414 will have three diagonals oriented in the same direction, because 5 and 5 are prime numbers, althought 9 is not. On the other side, combination 313 has no prime sum pair, but the sum of all three digits is a prime number.
I think that the sample with six numbers is not sufficient for such a puzzle. Thanks for your answer. Matus

For diagonal directions, always consider the whole connected group (all cells touching by corner), not parts. So 414=9 is not prime sum and neither of three cells will be marked. And 313=7 is prime sum so all three cells will be marked.

its says sum of each group of horizontally or vertically adjacent cells must be a prime number
But in column 3 : 1+3 =4 is not prime how is it valid?
did i am missing something ?