Prime Triangle

A triangle with rows containing the numbers  that begins with 1, ends with , and such that the sum of each two consecutive entries being a prime. Rows 2 to 6 are unique,

(OEIS A051237) but there are multiple possibilities starting with row 7. For example, the two possibilities for row 7 are  and . The number of possible rows ending with , 2, ..., are 0, 1, 1, 1, 1, 1, 2, 4, 7, 24, 80, ... (OEIS A036440).

REFERENCES:

Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 106, 1994.

Kenney, M. J. "Student Math Notes." NCTM News Bulletin. Nov. 1986.

Sloane, N. J. A. Sequences A036440 and A051237 in "The On-Line Encyclopedia of Integer Sequences."