Some times that's good enough. In particular, can you find prime numbers in the same sense as before. ISBN's and the labels on canned goods are examples of strings of digits that identify specific objects. A mistake in typing the digits will cause misidentification. The use of check digits and number theory.
Magic squares are square arrays of numbers whose row sums and column sums are constant.
Determining how to fill out magic squares is one area of investigation. Applications to scheduling of tournaments is another. A project could be Creating an annotated bibliography for articles related to number theory in these journals.