>>14180030Are you asking if there is a single base B in which all of the base 10 representations of prime numbers would be base B representations of composite numbers?
Besides 3, 5, and 7, which represent prime numbers in any base which includes those digits, of course.
Or can the base be different for each prime number?
Any base 10 representation with last digit not equal to 1 would be a base 210 representation of a composite number.
I think the base 10 representation of any N gives the base 10+N representation of a composite number, but I'm not sure.
I don't know of a single base that works for all.