diff --git a/man/coredump.conf.xml b/man/coredump.conf.xml
index 6392270543d5d..7cb71f80aa72a 100644
--- a/man/coredump.conf.xml
+++ b/man/coredump.conf.xml
@@ -85,7 +85,8 @@
 
         <listitem><para>The maximum size in bytes of a core which will be processed. Core dumps exceeding
         this size may be stored, but the backtrace will not be generated.  Like other sizes in this same
-        config file, the usual suffixes to the base of 1024 are allowed (B, K, M, G, T, P, and E).</para>
+        config file, the usual suffixes to the base of 1024 are allowed (B, K, M, G, T, P, and E). Defaults
+        to 1G on 32bit systems, 32G on 64bit systems.</para>
 
         <para>Setting <varname>Storage=none</varname> and <varname>ProcessSizeMax=0</varname>
         disables all coredump handling except for a log entry.</para>
@@ -96,8 +97,9 @@
         <term><varname>ExternalSizeMax=</varname></term>
         <term><varname>JournalSizeMax=</varname></term>
 
-        <listitem><para>The maximum (compressed or uncompressed) size in bytes of a core to be saved. Unit
-        suffixes are allowed just as in <option>ProcessSizeMax=</option>.</para></listitem>
+        <listitem><para>The maximum (compressed or uncompressed) size in bytes of a core to be saved in
+        separate files on disk (default: 1G on 32bit, 32G on 64bit systems) or in the journal (default:
+        10M). Unit suffixes are allowed just as in <option>ProcessSizeMax=</option>.</para></listitem>
 
         <para><varname>ExternalSizeMax=infinity</varname> sets the core size to unlimited.</para>
       </varlistentry>
diff --git a/src/coredump/coredump.c b/src/coredump/coredump.c
index 20503cfd3b7a6..aac75dc552588 100644
--- a/src/coredump/coredump.c
+++ b/src/coredump/coredump.c
@@ -48,8 +48,14 @@
 #include "uid-alloc-range.h"
 #include "user-util.h"
 
-/* The maximum size up to which we process coredumps */
-#define PROCESS_SIZE_MAX ((uint64_t) (2LLU*1024LLU*1024LLU*1024LLU))
+/* The maximum size up to which we process coredumps. We use 1G on 32bit systems, and 32G on 64bit systems */
+#if __SIZEOF_POINTER__ == 4
+#define PROCESS_SIZE_MAX ((uint64_t) (1LLU*1024LLU*1024LLU*1024LLU))
+#elif __SIZEOF_POINTER__ == 8
+#define PROCESS_SIZE_MAX ((uint64_t) (32LLU*1024LLU*1024LLU*1024LLU))
+#else
+#error "Unexpected pointer size"
+#endif
 
 /* The maximum size up to which we leave the coredump around on disk */
 #define EXTERNAL_SIZE_MAX PROCESS_SIZE_MAX