Before trying the problem "note your opinion as to whether the observed pattern is known to continue, known not to continue, or not known at all."

After row 1, row n is obtained by inserting n between every pair of consecutive numbers that sum to n.

row 1:                  1 1
row 2:                 1 2 1
row 3:               1 3 2 3 1
row 4:            1 4 3  2  3 4 1
row 5:        1 5 4  3 5 2 5 3 4 5 1
row 6:   1  6  5 4  3 5  2  5  3  4 5  6 1
row 7: 1 7 6 5 4 7 3 5 7 2 7 5 3 7 4 5 6 7 1

The number of numbers in each row are 2, 3, 5, 7, 11, 13, 19...

Will they always be prime?