prime twin pairs yielding others

[Neil Fernandez]

Hi,

some prime twin pairs yield other prime twin pairs.

A twin pair separator is defined as the number sandwiched between two
primes that form a pair.

A twin pair is defined as yielding another twin pair if its sum is the
separator of another twin pair.

E.g. the sum of the pair 29,31 is 60. This is the separator of the pair
59,61. So 29,31 yields 59,61.

The sequence of lower primes in twin pairs that yield other twin pairs
begins:

5, 29, 659, 809, 2129, 2549, 3329, 3389, 5849, 6269, 10529, 33179,
41609, 44129, ...

Questions occurring:

- are all terms after the first term congruent to 29 (mod 30)?

- are there any twin pairs that yield twin pairs that themselves yield
  other twin pairs? If so, what is the smallest such pair?

:-)

Best wishes,

Neil
-- 
Neil Fernandez