1089 isn’t prime either (1089 is 9*121). I think this approach might not work in general because of the two relevant numbers for the first die needing to share a factor. The first prime has to be of the form A+B, where A= 2022/(prime divisor of 2022), and B = number that is a multiple of 2022/(product of 2 its primes) for the above method to work. But no such prime exists since A must be divisible by two of (2,3, 337), and B must also be divisible by two of (2,3, and 337), so they must share at least one non-one factor, and can’t be prime.
Well, I would clearly not last long among the pebble-sorters. I think your criticism is almost right.
Unless we can come up with some scheme whereby there’s only one prime left for particular regions, which I think would require 2*337+3*337+n*2*3 to be prime, which it looks to me like 1697=337*5+12 is.
Re problem 2:
1089 isn’t prime either (1089 is 9*121). I think this approach might not work in general because of the two relevant numbers for the first die needing to share a factor. The first prime has to be of the form A+B, where A= 2022/(prime divisor of 2022), and B = number that is a multiple of 2022/(product of 2 its primes) for the above method to work. But no such prime exists since A must be divisible by two of (2,3, 337), and B must also be divisible by two of (2,3, and 337), so they must share at least one non-one factor, and can’t be prime.
Oh, yeah, oops, I didn’t read it well enough. Anyway, it is right now, so ill leave my comment endorsing it.
[I edited in spoiler tags to the above comment.]
Well, I would clearly not last long among the pebble-sorters. I think your criticism is almost right.
Unless we can come up with some scheme whereby there’s only one prime left for particular regions, which I think would require 2*337+3*337+n*2*3 to be prime, which it looks to me like 1697=337*5+12 is.