What are the next two numbers in this sequence?

2, 5, 13, 31, 61, 109, ??, ??

(In reply to

Answer by K Sengupta)

Denoting the ith term as T(i), let us denote the jth prime as P(j).

Then,

There are T(i+1) is precisely P(i) prime numbers away from T(i), for i>=1

Thus, T(2) = 5 is P(1) = 2 prime numbers away from T(1),

T(3) = 13 is P(2) = 3 prime numbers away from T(2),

Accordingly, T(7) would be P(6) = 11 prime numbers away from T(6) = 109

Therefore, T(7) = 181

T(8) would be P(7) = 13 prime numbers away from T(7) = 181

Therefore, T(7) = 277.

Consequently, the required missing terms are: 181 and 277.