Puzzle 752. Palindromes as sum of the first k primes

Here you are asked to extend the OEIS sequence A038583, related to the palindromes resulting of the first k prime numbers.

In order you to start your own search from the latest results here are them:

From Sloane's OEIS (A038582, A038583, A038584)

       k               p(k)                    S(k)

           1                 2                         2  
           2                 3                         5  
           8                19                        77  
        7693             78347                 285080582  
        8510             87641                 352888253  
       12941            139241                854848458  
      146134           1959253              137372273731  
      637571           9564097             2939156519392  
    27198825         516916921          6833383883833386  
    53205635        1048924213         27155268786255172  
  6283318531      155353386241     477749724515427947774  
  7167375533      178196630873     625179415050514971526

Q. Send the next k, p(k) and S(k) palindrome value.