Move script hexification functions to primitives

diff --git a/bitcoin/examples/script.rs b/bitcoin/examples/script.rs
index 1c48e292..c308ca0e 100644
--- a/bitcoin/examples/script.rs
+++ b/bitcoin/examples/script.rs
@@ -9,8 +9,7 @@
 
 use bitcoin::consensus::encode;
 use bitcoin::key::WPubkeyHash;
-use bitcoin::script::{self, ScriptExt as _};
-use bitcoin::WitnessScriptBuf;
+use bitcoin::{script, WitnessScriptBuf};
 
 fn main() {
     let pk = "b472a266d0bd89c13706a4132ccfb16f7c3b9fcb".parse::<WPubkeyHash>().unwrap();
diff --git a/bitcoin/src/blockdata/script/borrowed.rs b/bitcoin/src/blockdata/script/borrowed.rs
index fbd2f65f..91ae73d4 100644
--- a/bitcoin/src/blockdata/script/borrowed.rs
+++ b/bitcoin/src/blockdata/script/borrowed.rs
@@ -2,7 +2,6 @@
 
 use core::fmt;
 
-use hex_unstable::DisplayHex as _;
 use internals::array::ArrayExt; // For `split_first`.
 use internals::ToU64 as _;
 
@@ -12,7 +11,7 @@ use super::{
     RedeemScriptSizeError, Script, ScriptHash, ScriptHashableTag, ScriptPubKey, ScriptSig,
     TapScript, WScriptHash, WitnessScript, WitnessScriptSizeError,
 };
-use crate::consensus::{self, Encodable};
+use crate::consensus::Encodable;
 use crate::key::{PublicKey, UntweakedPublicKey, WPubkeyHash};
 use crate::opcodes::all::*;
 use crate::opcodes::{self, Opcode};
@@ -138,20 +137,6 @@ internal_macros::define_extension_trait! {
         #[deprecated(since = "TBD", note = "use `to_hex_string_no_length_prefix` instead")]
         fn to_hex_string(&self) -> String { self.to_hex_string_no_length_prefix() }
 
-        /// Consensus encodes the script as lower-case hex.
-        ///
-        /// Consensus encoding includes a length prefix. To hex encode without the length prefix use
-        /// `to_hex_string_no_length_prefix`.
-        fn to_hex_string_prefixed(&self) -> String { consensus::encode::serialize_hex(self) }
-
-        /// Encodes the script as lower-case hex.
-        ///
-        /// This is **not** consensus encoding. The returned hex string will not include the length
-        /// prefix. See `to_hex_string_prefixed`.
-        fn to_hex_string_no_length_prefix(&self) -> String {
-            self.as_bytes().to_lower_hex_string()
-        }
-
         /// Returns the first opcode of the script (if there is any).
         fn first_opcode(&self) -> Option<Opcode> {
             self.as_bytes().first().copied().map(From::from)
diff --git a/bitcoin/src/blockdata/script/tests.rs b/bitcoin/src/blockdata/script/tests.rs
index 860f0baa..954c6f97 100644
--- a/bitcoin/src/blockdata/script/tests.rs
+++ b/bitcoin/src/blockdata/script/tests.rs
@@ -1086,8 +1086,6 @@ fn hex() {
     // touching the `bitcoin::consensus::encode` functions.
     use alloc::format;
 
-    use crate::blockdata::script::borrowed::ScriptExt as _;
-
     let consensus = "04deadbeef";
     let raw = "deadbeef";
 
diff --git a/primitives/src/script/borrowed.rs b/primitives/src/script/borrowed.rs
index a9456b1a..cab33adf 100644
--- a/primitives/src/script/borrowed.rs
+++ b/primitives/src/script/borrowed.rs
@@ -1,5 +1,7 @@
 // SPDX-License-Identifier: CC0-1.0
 
+#[cfg(all(feature = "hex", feature = "alloc"))]
+use alloc::string::String;
 use core::marker::PhantomData;
 use core::ops::{
     Bound, Index, Range, RangeFrom, RangeFull, RangeInclusive, RangeTo, RangeToInclusive,
@@ -119,6 +121,30 @@ impl<T> Script<T> {
     #[deprecated(since = "0.101.0", note = "use to_vec instead")]
     pub fn to_bytes(&self) -> Vec<u8> { self.to_vec() }
 
+    /// Consensus encodes the script as lower-case hex.
+    ///
+    /// Consensus encoding includes a length prefix. To hex encode without the length prefix use
+    /// `to_hex_string_no_length_prefix`.
+    #[cfg(all(feature = "hex", feature = "alloc"))]
+    pub fn to_hex_string_prefixed(&self) -> String {
+        use hex_unstable::{BytesToHexIter, Case};
+
+        // TODO: Can we remove allocation and use an iterator (like in `hex_codec`)?
+        let v = encoding::encode_to_vec(self);
+        BytesToHexIter::new(v.iter(), Case::Lower).collect()
+    }
+
+    /// Encodes the script as lower-case hex.
+    ///
+    /// This is **not** consensus encoding. The returned hex string will not include the length
+    /// prefix. See `to_hex_string_prefixed`.
+    #[cfg(all(feature = "hex", feature = "alloc"))]
+    pub fn to_hex_string_no_length_prefix(&self) -> String {
+        use hex_unstable::DisplayHex as _;
+
+        self.as_bytes().to_lower_hex_string()
+    }
+
     /// Returns the length in bytes of the script.
     #[inline]
     pub const fn len(&self) -> usize { self.as_bytes().len() }
diff --git a/primitives/src/script/owned.rs b/primitives/src/script/owned.rs
index d7019d36..7b7b57de 100644
--- a/primitives/src/script/owned.rs
+++ b/primitives/src/script/owned.rs
@@ -8,6 +8,8 @@ use core::ops::{Deref, DerefMut};
 #[cfg(feature = "arbitrary")]
 use arbitrary::{Arbitrary, Unstructured};
 use encoding::{ByteVecDecoder, ByteVecDecoderError, Decodable, Decoder};
+#[cfg(feature = "hex")]
+use crate::hex;
 use internals::write_err;
 
 use super::Script;