There are 143 primes between 100 and 999. We can, therefore, make 2,924,207 3x3 different squares with 3 horizontal primes. 50,621 of them have all three vertical numbers prime. About 1.7%.
There are 1061 primes between 1000 and 9999. We can, therefore, make 1,267,247,769,841 4x4 different squares with 4 horizontal primes. 406,721,511 of them have all four vertical numbers prime. About 0.032%.
I strongly suspect that this goes to 0, quite rapidly.
How many Sudokus can you get with 9 digit primes horizontally and vertically?
Not a single one. Which is quite obvious when you consider that you can’t have a 2, 4, 6, or 8 in the bottom row. But you have to, to have a Sudoku, by the definition.
I’m sure you’re right that the fraction of all-horizontals-prime grids that have all verticals prime tends to 0 as the size increases. But the number of such grids increases rapidly too.
There are 143 primes between 100 and 999. We can, therefore, make 2,924,207 3x3 different squares with 3 horizontal primes. 50,621 of them have all three vertical numbers prime. About 1.7%.
There are 1061 primes between 1000 and 9999. We can, therefore, make 1,267,247,769,841 4x4 different squares with 4 horizontal primes. 406,721,511 of them have all four vertical numbers prime. About 0.032%.
I strongly suspect that this goes to 0, quite rapidly.
How many Sudokus can you get with 9 digit primes horizontally and vertically?
Not a single one. Which is quite obvious when you consider that you can’t have a 2, 4, 6, or 8 in the bottom row. But you have to, to have a Sudoku, by the definition.
It’s a bit analogous situation here.
I’m sure you’re right that the fraction of all-horizontals-prime grids that have all verticals prime tends to 0 as the size increases. But the number of such grids increases rapidly too.