  Bitcoin is based on a P2P network that is used to propagate transactions and
blocks. While the P2P network design intends to hide the topology of the P2P
network, information about the topology is required to understand the network
from a scientific point of view. Thus, there is a natural tension between the
'desire' for unobservability on the one hand, and for observability on the
other hand. On a middle ground, one would at least be interested on some
statistical features of the Bitcoin network like the number of peers that
participate in the propagation of transactions and blocks. This number is
composed of the number of reachable peers that accept incoming connections and
unreachable peers that do not accept incoming connections. While the number of
reachable peers can be measured, it is inherently difficult to determine the
number of unreachable peers. Thus, the number of unreachable peers can only be
estimated based on some indicators. In this paper, we first define our
understanding of unreachable peers and then propose the PAL (Passive
Announcement Listening) method which gives an estimate of the number of
unreachable peers by observing ADDR messages that announce active IP addresses
in the network. The PAL method allows for detecting unreachable peers that
indicate that they provide services useful to the P2P network. In conjunction
with previous methods, the PAL method can help to get a better estimate of the
number of unreachable peers. We use the PAL method to analyze data from a
long-term measurement of the Bitcoin P2P network that gives insights into the
development of the number of unreachable peers over five years from 2015 to
2020. Results show that about 31,000 unreachable peers providing useful
services were active per day at the end of the year 2020. An empirical
validation indicates that the approach finds about 50 % of unreachable peers
that provide useful services.
