Right-truncatable Primes in Various Bases

Start here for terminology.

Here is a plot of the number of rtp's for each base, based upon the table below, and two functions which seem to bound above and below. Also in the table is the number of rtp leaders (leaf nodes, numbers with no children), the ratio of leaders, and the number of digits of the largest rtp in that base. The ratio of rtp's which are leaders can be seen to be roughly constant, independent of the base (~1/2.74). If you follow the links for each base, a complete record of how many rtps and leaders were found with each number of digits fan be found.

Using this rather inefficient GP script, you can find right-truncatable primes in arbitrary bases:

rtp(base)={
  local(pd=vector(eulerphi(base)),pdl=length(pd),fl=0,bl=[],sp=0,j,k);
  j=0;for(i=1,base-1,if(gcd(i,base)==1,j++;pd[j]=i));
  forprime(p=2,base-1,fl++;bl=concat(bl,[p]));
  while(length(bl)>0,
    nb=[];
    for(i=1,length(bl),
      p=bl[i]*base;
      k=0;
      for(j=1,pdl,if(ispseudoprime(p+pd[j]),k++;nb=concat(nb,[p+pd[j]])));
      fl+=k;sp+=!k
    );
    bl=nb
  );
  [fl,sp]
}