383 is a Palindrome number expressible as a sum of 3 consecutive palindromic primes:
383=101+131+151

Find additional samples like that or prove that none exists.

   10   for Pn=1 to 999999
   11   Nxprm=nxtprm(Nxprm)
   15    if Nxprm=Prv then stop
   16    if fnPalin(Nxprm) then
   17    :Sum=Sum-Ppp+Nxprm
   20    :Ppp=Pp:Pp=P:P=Nxprm
   40    :if fnPalin(Sum) then
   50       :print Ppp;Pp;P,Sum;:if prmdiv(Sum)=Sum then print "*":else print
   55    Prv=Nxprm
   60   next Pn:print Nxprm
  800   end
  900   '
 1000   fnPalin(N)
 1010     T=1:S=cutspc(str(N))
 1020     for I=1 to int(len(S)/2)
 1030       if mid(S,I,1)<>mid(S,len(S)+1-I,1) then T=0
 1040     next
 1050    return(T)

The first two lines of the below output are spurious due to the methodology used in the program. The remaining lines show the three successive palindromic primes, and the sum.  If the sum is also prime and asterisk (*) appears to the right of the line, as in the example, though the rules do not specifiy that primality is needed in the sum.

 0  0  2         2 *
 0  2  3         5 *
 101  131  151   383 *
 30103  30203  30403     90709 *
 31013  31513  32323     94849 *
 1120211  1123211  1126211       3369633
 1221221  1235321  1242421       3698963 *
 1300031  1303031  1311131       3914193
 15485857

The final, single, number shows the highest prime tested, the 999,999th prime.

Posted by Charlie on 2013-12-27 12:41:32