Senior Kangaroo 2024 Q20

Each cell in this cross-number can be filled with a non-zero digit so that all of the conditions in the clues are satisfied. The digits used are not necessarily distinct.

ACROSS

1. A prime.
2. The answer to this Kangaroo question.
3. Shares a two-digit common factor with 1 DOWN.

DOWN

1. The sum of two different sixth powers.
2. 101 less than a square number.
3. The sum of all the digits in this crossnumber, once correctly completed.