diff --git a/Doc/library/stdtypes.rst b/Doc/library/stdtypes.rst
index 01c9b9a5cf4106..be092364047852 100644
--- a/Doc/library/stdtypes.rst
+++ b/Doc/library/stdtypes.rst
@@ -5493,7 +5493,7 @@ When an operation would exceed the limit, a :exc:`ValueError` is raised:
    >>> _ = int('2' * 5432)
    Traceback (most recent call last):
    ...
-   ValueError: Exceeds the limit (4300) for integer string conversion: value has 5432 digits.
+   ValueError: Exceeds the limit (4300) for integer string conversion: value has 5432 digits; use sys.set_int_max_str_digits() to increase the limit.
    >>> i = int('2' * 4300)
    >>> len(str(i))
    4300
@@ -5501,7 +5501,7 @@ When an operation would exceed the limit, a :exc:`ValueError` is raised:
    >>> len(str(i_squared))
    Traceback (most recent call last):
    ...
-   ValueError: Exceeds the limit (4300) for integer string conversion: value has 8599 digits.
+   ValueError: Exceeds the limit (4300) for integer string conversion: value has 8599 digits; use sys.set_int_max_str_digits() to increase the limit.
    >>> len(hex(i_squared))
    7144
    >>> assert int(hex(i_squared), base=16) == i*i  # Hexadecimal is unlimited.
diff --git a/Misc/NEWS.d/next/Core and Builtins/2022-09-16-19-02-40.gh-issue-95778.cJmnst.rst b/Misc/NEWS.d/next/Core and Builtins/2022-09-16-19-02-40.gh-issue-95778.cJmnst.rst
new file mode 100644
index 00000000000000..ebf63778a605d7
--- /dev/null
+++ b/Misc/NEWS.d/next/Core and Builtins/2022-09-16-19-02-40.gh-issue-95778.cJmnst.rst	
@@ -0,0 +1,3 @@
+When :exc:`ValueError` is raised if an integer is larger than the limit,
+mention the :func:`sys.set_int_max_str_digits` function in the error message.
+Patch by Victor Stinner.
diff --git a/Objects/longobject.c b/Objects/longobject.c
index cb52f82687af28..c0bade18221843 100644
--- a/Objects/longobject.c
+++ b/Objects/longobject.c
@@ -36,8 +36,8 @@ medium_value(PyLongObject *x)
 #define IS_SMALL_INT(ival) (-_PY_NSMALLNEGINTS <= (ival) && (ival) < _PY_NSMALLPOSINTS)
 #define IS_SMALL_UINT(ival) ((ival) < _PY_NSMALLPOSINTS)
 
-#define _MAX_STR_DIGITS_ERROR_FMT_TO_INT "Exceeds the limit (%d) for integer string conversion: value has %zd digits"
-#define _MAX_STR_DIGITS_ERROR_FMT_TO_STR "Exceeds the limit (%d) for integer string conversion"
+#define _MAX_STR_DIGITS_ERROR_FMT_TO_INT "Exceeds the limit (%d) for integer string conversion: value has %zd digits; use sys.set_int_max_str_digits() to increase the limit"
+#define _MAX_STR_DIGITS_ERROR_FMT_TO_STR "Exceeds the limit (%d) for integer string conversion; use sys.set_int_max_str_digits() to increase the limit"
 
 static inline void
 _Py_DECREF_INT(PyLongObject *op)