Which of the following numbers will replace the question mark (?) in the given series?4, 7, 17, 38, 72, 123, 193, 286, 408, ?

Let's find the difference between consecutive terms in the series:$7-4=3$$17-7=10$$38-17=21$$72-38=34$$123-72=51$$193-123=70$$286-193=93$$408-286=122$ Now let's compute the second-level differences (differences of differences):$10-3=7$$21-10=11$$34-21=13$$51-34=17$$70-51=19$$93-70=23$$122-93=29$ Notice that the second-level differences are consecutive prime numbers: $7,11,13,17,19,23,29$.The next prime number after $29$ is $31$.Therefore:Next first-level difference = $122+31=153$ Missing number = $408+153=561$