KöMaL 2025 K850

The teacher has written a two-digit positive prime number and a non-zero digit on the blackboard. Each one of Sanyi, Kati, and Joli has created a three-digit number from the numbers on the blackboard. Sanyi has written the digit behind the prime number written on the blackboard, Kati has written the digit between the digits of the given prime number, and Joli has written the digit in front of the given prime number. Sanyi's number was 45 more than Kati's number and 225 more than Joli's number. Find the prime number and the digit chosen by the teacher.