diff --git a/docs/VictoriaLogs/CHANGELOG.md b/docs/VictoriaLogs/CHANGELOG.md
index fd50f0c71..974f4dd08 100644
--- a/docs/VictoriaLogs/CHANGELOG.md
+++ b/docs/VictoriaLogs/CHANGELOG.md
@@ -24,6 +24,8 @@ according to [these docs](https://docs.victoriametrics.com/VictoriaLogs/QuickSta
 * FEATURE: add support for calculating the number of matching logs and the number of logs with non-empty [fields](https://docs.victoriametrics.com/victorialogs/keyconcepts/#data-model). Grouping by arbitrary set of [log fields](https://docs.victoriametrics.com/victorialogs/keyconcepts/#data-model) is supported. See [these docs](https://docs.victoriametrics.com/victorialogs/logsql/#stats) for details.
 * FEATURE: add support for limiting the number of returned results. See [these docs](https://docs.victoriametrics.com/victorialogs/logsql/#limiters).
 * FEATURE: optimize performance for [LogsQL query](https://docs.victoriametrics.com/victorialogs/logsql/), which contains multiple filters for [words](https://docs.victoriametrics.com/victorialogs/logsql/#word-filter) or [phrases](https://docs.victoriametrics.com/victorialogs/logsql/#phrase-filter) delimited with [`AND` operator](https://docs.victoriametrics.com/victorialogs/logsql/#logical-filter). For example, `foo AND bar` query must find [log messages](https://docs.victoriametrics.com/victorialogs/keyconcepts/#message-field) with `foo` and `bar` words at faster speed.
+* FEATURE: allow using `_` inside numbers. For example, `score:range[1_000, 5_000_000]` for [`range` filter](https://docs.victoriametrics.com/victorialogs/logsql/#range-filter).
+* FEATURE: allow numbers in hexadecimal and binary form. For example, `response_size:range[0xff, 0b10001101101]` for [`range` filter](https://docs.victoriametrics.com/victorialogs/logsql/#range-filter).
 
 * BUGFIX: prevent from additional CPU usage for up to a few seconds after canceling the query.
 * BUGFIX: prevent from returning log entries with emtpy `_stream` field in the form `"_stream":""` in [search query results](https://docs.victoriametrics.com/victorialogs/querying/). See [this issue](https://github.com/VictoriaMetrics/VictoriaMetrics/issues/6042).
diff --git a/docs/VictoriaLogs/LogsQL.md b/docs/VictoriaLogs/LogsQL.md
index be7cbeb18..265d74009 100644
--- a/docs/VictoriaLogs/LogsQL.md
+++ b/docs/VictoriaLogs/LogsQL.md
@@ -827,6 +827,12 @@ parentheses with square brackets. For example:
 - `range(1, 10]` includes `10` in the matching range
 - `range[1, 10]` includes `1` and `10` in the matching range
 
+The range boundaries can be expressed in the following forms:
+
+- Hexadecimal form. For example, `range(0xff, 0xABCD)`.
+- Binary form. Form example, `range(0b100110, 0b11111101)`
+- Integer form with `_` delimiters for better readability. For example, `range(1_000, 2_345_678)`.
+
 Note that the `range()` filter doesn't match [log fields](https://docs.victoriametrics.com/VictoriaLogs/keyConcepts.html#data-model)
 with non-numeric values alongside numeric values. For example, `range(1, 10)` doesn't match `the request took 4.2 seconds`
 [log message](https://docs.victoriametrics.com/VictoriaLogs/keyConcepts.html#message-field), since the `4.2` number is surrounded by other text.
@@ -938,6 +944,19 @@ This query doesn't match the following log messages:
 - `foo`, since it is too short
 - `foo bar baz abc`, sinc it is too long
 
+It is possible to use `inf` as the upper bound. For example, the following query matches [log messages](https://docs.victoriametrics.com/VictoriaLogs/keyConcepts.html#message-field)
+with the length bigger or equal to 5 chars:
+
+```logsql
+len_range(5, inf)
+```
+
+The range boundaries can be expressed in the following forms:
+
+- Hexadecimal form. For example, `len_range(0xff, 0xABCD)`.
+- Binary form. Form example, `len_range(0b100110, 0b11111101)`
+- Integer form with `_` delimiters for better readability. For example, `len_range(1_000, 2_345_678)`.
+
 By default the `len_range()` is applied to the [`_msg` field](https://docs.victoriametrics.com/VictoriaLogs/keyConcepts.html#message-field).
 Put the [field name](https://docs.victoriametrics.com/VictoriaLogs/keyConcepts.html#data-model) in front of the `len_range()` in order to apply
 the filter to the needed field. For example, the following query matches log entries with the `foo` field length in the range `[10, 20]` chars:
diff --git a/lib/logstorage/filters.go b/lib/logstorage/filters.go
index acc638b3f..48b8c0fec 100644
--- a/lib/logstorage/filters.go
+++ b/lib/logstorage/filters.go
@@ -1083,10 +1083,12 @@ type lenRangeFilter struct {
 	fieldName string
 	minLen    uint64
 	maxLen    uint64
+
+	stringRepr string
 }
 
 func (rf *lenRangeFilter) String() string {
-	return quoteFieldNameIfNeeded(rf.fieldName) + fmt.Sprintf("len_range(%d,%d)", rf.minLen, rf.maxLen)
+	return quoteFieldNameIfNeeded(rf.fieldName) + "len_range" + rf.stringRepr
 }
 
 func (rf *lenRangeFilter) apply(bs *blockSearch, bm *filterBitmap) {
diff --git a/lib/logstorage/parser.go b/lib/logstorage/parser.go
index 3c16e50fb..bac0288a3 100644
--- a/lib/logstorage/parser.go
+++ b/lib/logstorage/parser.go
@@ -522,18 +522,21 @@ func parseLenRangeFilter(lex *lexer, fieldName string) (filter, error) {
 		if len(args) != 2 {
 			return nil, fmt.Errorf("unexpected number of args for %s(); got %d; want 2", funcName, len(args))
 		}
-		minLen, err := strconv.ParseUint(args[0], 10, 64)
+		minLen, err := parseUint(args[0])
 		if err != nil {
 			return nil, fmt.Errorf("cannot parse minLen at %s(): %w", funcName, err)
 		}
-		maxLen, err := strconv.ParseUint(args[1], 10, 64)
+		maxLen, err := parseUint(args[1])
 		if err != nil {
 			return nil, fmt.Errorf("cannot parse maxLen at %s(): %w", funcName, err)
 		}
+		stringRepr := "(" + args[0] + ", " + args[1] + ")"
 		rf := &lenRangeFilter{
 			fieldName: fieldName,
 			minLen:    minLen,
 			maxLen:    maxLen,
+
+			stringRepr: stringRepr,
 		}
 		return rf, nil
 	})
@@ -715,7 +718,7 @@ func parseRangeFilter(lex *lexer, fieldName string) (filter, error) {
 		stringRepr += "("
 		minValue = math.Nextafter(minValue, math.Inf(1))
 	}
-	stringRepr += minValueStr + "," + maxValueStr
+	stringRepr += minValueStr + ", " + maxValueStr
 	if includeMaxValue {
 		stringRepr += "]"
 	} else {
@@ -737,6 +740,12 @@ func parseFloat64(lex *lexer) (float64, string, error) {
 	s := getCompoundToken(lex)
 	f, err := strconv.ParseFloat(s, 64)
 	if err != nil {
+		// Try parsing s as integer.
+		// This handles 0x..., 0b... and 0... prefixes.
+		n, err := parseInt(s)
+		if err == nil {
+			return float64(n), s, nil
+		}
 		return 0, "", fmt.Errorf("cannot parse %q as float64: %w", lex.token, err)
 	}
 	return f, s, nil
@@ -1170,3 +1179,21 @@ var reservedKeywords = func() map[string]struct{} {
 	}
 	return m
 }()
+
+func parseUint(s string) (uint64, error) {
+	if strings.EqualFold(s, "inf") || strings.EqualFold(s, "+inf") {
+		return math.MaxUint64, nil
+	}
+	return strconv.ParseUint(s, 0, 64)
+}
+
+func parseInt(s string) (int64, error) {
+	switch {
+	case strings.EqualFold(s, "inf"), strings.EqualFold(s, "+inf"):
+		return math.MaxInt64, nil
+	case strings.EqualFold(s, "-inf"):
+		return math.MinInt64, nil
+	default:
+		return strconv.ParseInt(s, 0, 64)
+	}
+}
diff --git a/lib/logstorage/parser_test.go b/lib/logstorage/parser_test.go
index 62605dd86..9fbb9ac5e 100644
--- a/lib/logstorage/parser_test.go
+++ b/lib/logstorage/parser_test.go
@@ -743,16 +743,23 @@ func TestParseQuerySuccess(t *testing.T) {
 	f(`ipv4_range(1.2.3.4,)`, `ipv4_range(1.2.3.4, 1.2.3.4)`)
 
 	// len_range filter
-	f(`len_range(10, 20)`, `len_range(10,20)`)
-	f(`foo:len_range("10", 20, )`, `foo:len_range(10,20)`)
+	f(`len_range(10, 20)`, `len_range(10, 20)`)
+	f(`foo:len_range("10", 20, )`, `foo:len_range(10, 20)`)
+	f(`len_RANGe(10, inf)`, `len_range(10, inf)`)
+	f(`len_range(10, +InF)`, `len_range(10, +InF)`)
+	f(`len_range(10, 1_000_000)`, `len_range(10, 1_000_000)`)
+	f(`len_range(0x10,0b100101)`, `len_range(0x10, 0b100101)`)
 
 	// range filter
-	f(`range(1.234, 5656.43454)`, `range(1.234,5656.43454)`)
-	f(`foo:range(-2343.344, 2343.4343)`, `foo:range(-2343.344,2343.4343)`)
-	f(`range(-1.234e-5  , 2.34E+3)`, `range(-1.234e-5,2.34E+3)`)
-	f(`range[123, 456)`, `range[123,456)`)
-	f(`range(123, 445]`, `range(123,445]`)
-	f(`range("1.234e-4", -23)`, `range(1.234e-4,-23)`)
+	f(`range(1.234, 5656.43454)`, `range(1.234, 5656.43454)`)
+	f(`foo:range(-2343.344, 2343.4343)`, `foo:range(-2343.344, 2343.4343)`)
+	f(`range(-1.234e-5  , 2.34E+3)`, `range(-1.234e-5, 2.34E+3)`)
+	f(`range[123, 456)`, `range[123, 456)`)
+	f(`range(123, 445]`, `range(123, 445]`)
+	f(`range("1.234e-4", -23)`, `range(1.234e-4, -23)`)
+	f(`range(1_000, 0o7532)`, `range(1_000, 0o7532)`)
+	f(`range(0x1ff, inf)`, `range(0x1ff, inf)`)
+	f(`range(-INF,+inF)`, `range(-INF, +inF)`)
 
 	// re filter
 	f("re('foo|ba(r.+)')", `re("foo|ba(r.+)")`)
diff --git a/lib/logstorage/pipes.go b/lib/logstorage/pipes.go
index 1a4db2794..6afc417b0 100644
--- a/lib/logstorage/pipes.go
+++ b/lib/logstorage/pipes.go
@@ -829,7 +829,7 @@ func parseHeadPipe(lex *lexer) (*headPipe, error) {
 	if !lex.mustNextToken() {
 		return nil, fmt.Errorf("missing the number of head rows to return")
 	}
-	n, err := strconv.ParseUint(lex.token, 10, 64)
+	n, err := parseUint(lex.token)
 	if err != nil {
 		return nil, fmt.Errorf("cannot parse the number of head rows to return %q: %w", lex.token, err)
 	}
@@ -896,7 +896,7 @@ func parseSkipPipe(lex *lexer) (*skipPipe, error) {
 	if !lex.mustNextToken() {
 		return nil, fmt.Errorf("missing the number of rows to skip")
 	}
-	n, err := strconv.ParseUint(lex.token, 10, 64)
+	n, err := parseUint(lex.token)
 	if err != nil {
 		return nil, fmt.Errorf("cannot parse the number of rows to skip %q: %w", lex.token, err)
 	}