diff --git a/hypothesis-python/RELEASE.rst b/hypothesis-python/RELEASE.rst
new file mode 100644
index 0000000000..ee287870fe
--- /dev/null
+++ b/hypothesis-python/RELEASE.rst
@@ -0,0 +1,10 @@
+RELEASE_TYPE: minor
+
+Did you know that of the 2\ :superscript:`64` possible floating-point numbers,
+2\ :superscript:`53` of them are ``nan`` - and Python prints them all the same way?
+
+While nans *usually* have all zeros in the sign bit and mantissa, this
+`isn't always true <https://wingolog.org/archives/2011/05/18/value-representation-in-javascript-implementations>`__,
+and :wikipedia:`'signaling' nans might trap or error <https://en.wikipedia.org/wiki/NaN#Signaling_NaN>`.
+To help distinguish such errors in e.g. CI logs, Hypothesis now prints ``-nan`` for
+negative nans, and adds a comment like ``# Saw 3 signaling NaNs`` if applicable.
diff --git a/hypothesis-python/src/hypothesis/strategies/_internal/numbers.py b/hypothesis-python/src/hypothesis/strategies/_internal/numbers.py
index 328a94bc9b..6f726a022d 100644
--- a/hypothesis-python/src/hypothesis/strategies/_internal/numbers.py
+++ b/hypothesis-python/src/hypothesis/strategies/_internal/numbers.py
@@ -147,6 +147,9 @@ def integers(
     return IntegersStrategy(min_value, max_value)
 
 
+SIGNALING_NAN = int_to_float(0x7FF8_0000_0000_0001)  # nonzero mantissa
+assert math.isnan(SIGNALING_NAN) and math.copysign(1, SIGNALING_NAN) == 1
+
 NASTY_FLOATS = sorted(
     [
         0.0,
@@ -170,7 +173,8 @@ def integers(
     ]
     + [2.0 ** -n for n in (24, 14, 149, 126)]  # minimum (sub)normals for float16,32
     + [float_info.min / n for n in (2, 10, 1000, 100_000)]  # subnormal in float64
-    + [math.inf, math.nan] * 5,
+    + [math.inf, math.nan] * 5
+    + [SIGNALING_NAN],
     key=flt.float_to_lex,
 )
 NASTY_FLOATS = list(map(float, NASTY_FLOATS))
diff --git a/hypothesis-python/src/hypothesis/vendor/pretty.py b/hypothesis-python/src/hypothesis/vendor/pretty.py
index 688a8a2277..8973fff1a7 100644
--- a/hypothesis-python/src/hypothesis/vendor/pretty.py
+++ b/hypothesis-python/src/hypothesis/vendor/pretty.py
@@ -70,10 +70,12 @@ def _repr_pretty_(self, p, cycle):
 import datetime
 import platform
 import re
+import struct
 import types
 from collections import deque
 from contextlib import contextmanager
 from io import StringIO
+from math import copysign, isnan
 
 __all__ = [
     "pretty",
@@ -161,6 +163,8 @@ def __init__(
         self.group_queue = GroupQueue(root_group)
         self.indentation = 0
 
+        self.snans = 0
+
     def _break_outer_groups(self):
         while self.max_width < self.output_width + self.buffer_width:
             group = self.group_queue.deq()
@@ -266,6 +270,12 @@ def end_group(self, dedent=0, close=""):
 
     def flush(self):
         """Flush data that is left in the buffer."""
+        if self.snans:
+            # Reset self.snans *before* calling breakable(), which might flush()
+            snans = self.snans
+            self.snans = 0
+            self.breakable("  ")
+            self.text(f"# Saw {snans} signaling NaN" + "s" * (snans > 1))
         for data in self.buffer:
             self.output_width += data.output(self.output, self.output_width)
         self.buffer.clear()
@@ -735,10 +745,20 @@ def _exception_pprint(obj, p, cycle):
     p.end_group(step, ")")
 
 
+def _repr_float_counting_nans(obj, p, cycle):
+    if isnan(obj) and hasattr(p, "snans"):
+        if struct.pack("!d", abs(obj)) != struct.pack("!d", float("nan")):
+            p.snans += 1
+        if copysign(1.0, obj) == -1.0:
+            p.text("-nan")
+            return
+    p.text(repr(obj))
+
+
 #: printers for builtin types
 _type_pprinters = {
     int: _repr_pprint,
-    float: _repr_pprint,
+    float: _repr_float_counting_nans,
     str: _repr_pprint,
     tuple: _seq_pprinter_factory("(", ")", tuple),
     list: _seq_pprinter_factory("[", "]", list),
diff --git a/hypothesis-python/tests/cover/test_pretty.py b/hypothesis-python/tests/cover/test_pretty.py
index 4294812415..758d53baac 100644
--- a/hypothesis-python/tests/cover/test_pretty.py
+++ b/hypothesis-python/tests/cover/test_pretty.py
@@ -59,6 +59,7 @@
 import pytest
 
 from hypothesis.internal.compat import PYPY
+from hypothesis.strategies._internal.numbers import SIGNALING_NAN
 from hypothesis.vendor import pretty
 
 
@@ -622,3 +623,17 @@ def test_empty_printer():
 
 def test_breakable_at_group_boundary():
     assert "\n" in pretty.pretty([[], "000000"], max_width=5)
+
+
+@pytest.mark.parametrize(
+    "obj, rep",
+    [
+        (float("nan"), "nan"),
+        (-float("nan"), "-nan"),
+        (SIGNALING_NAN, "nan  # Saw 1 signaling NaN"),
+        (-SIGNALING_NAN, "-nan  # Saw 1 signaling NaN"),
+        ((SIGNALING_NAN, SIGNALING_NAN), "(nan, nan)  # Saw 2 signaling NaNs"),
+    ],
+)
+def test_nan_reprs(obj, rep):
+    assert pretty.pretty(obj) == rep
diff --git a/hypothesis-python/tests/nocover/test_floating.py b/hypothesis-python/tests/nocover/test_floating.py
index a84c9dba8a..808d61e479 100644
--- a/hypothesis-python/tests/nocover/test_floating.py
+++ b/hypothesis-python/tests/nocover/test_floating.py
@@ -21,9 +21,10 @@
 import pytest
 
 from hypothesis import HealthCheck, assume, given, settings
-from hypothesis.internal.floats import next_down
+from hypothesis.internal.floats import float_to_int, next_down
 from hypothesis.strategies import data, floats, lists
 
+from tests.common.debug import find_any
 from tests.common.utils import fails
 
 TRY_HARDER = settings(
@@ -161,3 +162,16 @@ def test_floats_are_in_range(x, y, data):
 
     t = data.draw(floats(x, y))
     assert x <= t <= y
+
+
+@pytest.mark.parametrize("neg", [False, True])
+@pytest.mark.parametrize("snan", [False, True])
+def test_can_find_negative_and_signaling_nans(neg, snan):
+    find_any(
+        floats().filter(math.isnan),
+        lambda x: (
+            snan is (float_to_int(abs(x)) != float_to_int(float("nan")))
+            and neg is (math.copysign(1, x) == -1)
+        ),
+        settings=TRY_HARDER,
+    )