The core file is normally called core and is located in the current working directory of the process. However, there is a long list of reasons why a core file would not be generated, and it may be located somewhere else entirely, under a different name. See the core.5 man page for details:
DESCRIPTION
The default action of certain signals is to cause a process to
terminate and produce a core dump file, a disk file containing an
image of the process's memory at the time of termination. This image
can be used in a debugger (e.g., gdb(1)) to inspect the state of the
program at the time that it terminated. A list of the signals which
cause a process to dump core can be found in signal(7).
...
There are various circumstances in which a core dump file is not produced:
* The process does not have permission to write the core file. (By
default, the core file is called core or core.pid, where pid is
the ID of the process that dumped core, and is created in the
current working directory. See below for details on naming.)
Writing the core file will fail if the directory in which it is to
be created is nonwritable, or if a file with the same name exists
and is not writable or is not a regular file (e.g., it is a
directory or a symbolic link).
* A (writable, regular) file with the same name as would be used for
the core dump already exists, but there is more than one hard link
to that file.
* The filesystem where the core dump file would be created is full;
or has run out of inodes; or is mounted read-only; or the user has
reached their quota for the filesystem.
* The directory in which the core dump file is to be created does
not exist.
* The RLIMIT_CORE (core file size) or RLIMIT_FSIZE (file size)
resource limits for the process are set to zero; see getrlimit(2)
and the documentation of the shell's ulimit command (limit in
csh(1)).
* The binary being executed by the process does not have read
permission enabled.
* The process is executing a set-user-ID (set-group-ID) program that
is owned by a user (group) other than the real user (group) ID of
the process, or the process is executing a program that has file
capabilities (see capabilities(7)). (However, see the description
of the prctl(2) PR_SET_DUMPABLE operation, and the description of
the /proc/sys/fs/suid_dumpable file in proc(5).)
* (Since Linux 3.7) The kernel was configured without the
CONFIG_COREDUMP option.
In addition, a core dump may exclude part of the address space of the
process if the madvise(2) MADV_DONTDUMP flag was employed.
Naming of core dump files
By default, a core dump file is named core, but the
/proc/sys/kernel/core_pattern file (since Linux 2.6 and 2.4.21) can
be set to define a template that is used to name core dump files.
The template can contain % specifiers which are substituted by the
following values when a core file is created:
%% a single % character
%c core file size soft resource limit of crashing process (since
Linux 2.6.24)
%d dump mode—same as value returned by prctl(2) PR_GET_DUMPABLE
(since Linux 3.7)
%e executable filename (without path prefix)
%E pathname of executable, with slashes ('/') replaced by
exclamation marks ('!') (since Linux 3.0).
%g (numeric) real GID of dumped process
%h hostname (same as nodename returned by uname(2))
%i TID of thread that triggered core dump, as seen in the PID
namespace in which the thread resides (since Linux 3.18)
%I TID of thread that triggered core dump, as seen in the
initial PID namespace (since Linux 3.18)
%p PID of dumped process, as seen in the PID namespace in which
the process resides
%P PID of dumped process, as seen in the initial PID namespace
(since Linux 3.12)
%s number of signal causing dump
%t time of dump, expressed as seconds since the Epoch,
1970-01-01 00:00:00 +0000 (UTC)
%u (numeric) real UID of dumped process
gdb path-to-your-binary path-to-corefile, theninfo stackfollowed byCtrl-d. The only worrying thing is that core-dumping is a usual thing for you.