diff --git a/recipes/openblas/all/conandata.yml b/recipes/openblas/all/conandata.yml
index 85e4fee5631f1..74a69a147b022 100644
--- a/recipes/openblas/all/conandata.yml
+++ b/recipes/openblas/all/conandata.yml
@@ -1,4 +1,7 @@
 sources:
+  "0.3.28":
+    url: "https://github.com/xianyi/OpenBLAS/archive/v0.3.28.tar.gz"
+    sha256: "f1003466ad074e9b0c8d421a204121100b0751c96fc6fcf3d1456bd12f8a00a1"
   "0.3.27":
     url: "https://github.com/xianyi/OpenBLAS/archive/v0.3.27.tar.gz"
     sha256: "aa2d68b1564fe2b13bc292672608e9cdeeeb6dc34995512e65c3b10f4599e897"
@@ -14,18 +17,3 @@ sources:
   "0.3.20":
     url: "https://github.com/xianyi/OpenBLAS/archive/v0.3.20.tar.gz"
     sha256: "8495c9affc536253648e942908e88e097f2ec7753ede55aca52e5dead3029e3c"
-  "0.3.17":
-    url: "https://github.com/xianyi/OpenBLAS/archive/v0.3.17.tar.gz"
-    sha256: "df2934fa33d04fd84d839ca698280df55c690c86a5a1133b3f7266fce1de279f"
-  "0.3.15":
-    url: "https://github.com/xianyi/OpenBLAS/archive/v0.3.15.tar.gz"
-    sha256: "30a99dec977594b387a17f49904523e6bc8dd88bd247266e83485803759e4bbe"
-  "0.3.13":
-    url: "https://github.com/xianyi/OpenBLAS/archive/v0.3.13.tar.gz"
-    sha256: "79197543b17cc314b7e43f7a33148c308b0807cd6381ee77f77e15acf3e6459e"
-  "0.3.12":
-    url: "https://github.com/xianyi/OpenBLAS/archive/v0.3.12.tar.gz"
-    sha256: "65a7d3a4010a4e3bd5c0baa41a234797cd3a1735449a4a5902129152601dc57b"
-  "0.3.10":
-    url: "https://github.com/xianyi/OpenBLAS/archive/v0.3.10.tar.gz"
-    sha256: "0484d275f87e9b8641ff2eecaa9df2830cbe276ac79ad80494822721de6e1693"
diff --git a/recipes/openblas/all/conanfile.py b/recipes/openblas/all/conanfile.py
index 6fcc5d83048b9..de3605b3e524e 100644
--- a/recipes/openblas/all/conanfile.py
+++ b/recipes/openblas/all/conanfile.py
@@ -3,11 +3,10 @@
 from conan.tools.apple import fix_apple_shared_install_name
 from conan.tools.build import cross_building
 from conan.tools.cmake import CMake, CMakeToolchain, cmake_layout
-from conan.tools.files import copy, get, replace_in_file, rmdir
+from conan.tools.files import copy, get, rmdir
 from conan.tools.microsoft import is_msvc_static_runtime, is_msvc
 from conan.tools.scm import Version
 import os
-import textwrap
 
 required_conan_version = ">=1.53.0"
 
@@ -108,11 +107,6 @@ def _fortran_compiler(self):
     def config_options(self):
         if self.settings.os == "Windows":
             del self.options.fPIC
-        # When no Fortran compiler is available, OpenBLAS builds LAPACK from an f2c-converted copy of LAPACK unless the NO_LAPACK option is specified.
-        # This is not available before v0.3.21.
-        if Version(self.version) < "0.3.21":
-            self.options.build_lapack = False
-            self.options.build_relapack = False
 
     def configure(self):
         if self.options.shared:
@@ -164,14 +158,10 @@ def generate(self):
         tc.variables["BUILD_TESTING"] = False
 
         tc.variables["NOFORTRAN"] = not self.options.build_lapack
-        # This checks explicit user-specified fortran compiler
         if self.options.build_lapack and not self._fortran_compiler:
-            if Version(self.version) < "0.3.21":
-                self.output.warning("Building with LAPACK support requires a Fortran compiler.")
-            else:
-                tc.variables["C_LAPACK"] = True
-                tc.variables["NOFORTRAN"] = True
-                self.output.info("Building LAPACK without a Fortran compiler")
+            tc.variables["C_LAPACK"] = True
+            tc.variables["NOFORTRAN"] = True
+            self.output.info("Building LAPACK without a Fortran compiler")
 
         tc.variables["BUILD_WITHOUT_LAPACK"] = not self.options.build_lapack
         tc.variables["BUILD_RELAPACK"] = self.options.build_relapack
@@ -190,46 +180,14 @@ def generate(self):
             tc.cache_variables["TARGET"] = self.options.target
 
         tc.cache_variables["CMAKE_POLICY_DEFAULT_CMP0077"] = "NEW"
-        tc.generate()
 
-    def _patch_sources(self):
-        if Version(self.version) <= "0.3.15":
-            replace_in_file(self, os.path.join(self.source_folder, "cmake", "utils.cmake"),
-                "set(obj_defines ${defines_in})", textwrap.dedent("""\
-                 set(obj_defines ${defines_in})
+        # Fix a fatal compiler warning on GCC 14
+        # https://github.com/OpenMathLib/OpenBLAS/pull/4894
+        tc.extra_cflags.append("-Wno-error=incompatible-pointer-types")
 
-                 list(FIND obj_defines "RC" def_idx)
-                 if (${def_idx} GREATER -1)
-                   list(REMOVE_ITEM obj_defines "RC")
-                   list(APPEND obj_defines "RC=RC")
-                 endif ()
-                 list(FIND obj_defines "CR" def_idx)
-                 if (${def_idx} GREATER -1)
-                   list(REMOVE_ITEM obj_defines "CR")
-                   list(APPEND obj_defines "CR=CR")
-                 endif ()"""))
-        if Version(self.version) < "0.3.21":
-            f_check_cmake = os.path.join(self.source_folder, "cmake", "f_check.cmake")
-            if Version(self.version) >= "0.3.12":
-                replace_in_file(self, f_check_cmake,
-                                'message(STATUS "No Fortran compiler found, can build only BLAS but not LAPACK")',
-                                'message(FATAL_ERROR "No Fortran compiler found. Cannot build with LAPACK.")')
-            else:
-                replace_in_file(self, f_check_cmake,
-                    "enable_language(Fortran)",
-                    textwrap.dedent("""\
-                        include(CheckLanguage)
-                        check_language(Fortran)
-                        if(CMAKE_Fortran_COMPILER)
-                          enable_language(Fortran)
-                        else()
-                          message(FATAL_ERROR "No Fortran compiler found. Cannot build with LAPACK.")
-                          set (NOFORTRAN 1)
-                          set (NO_LAPACK 1)
-                        endif()"""))
+        tc.generate()
 
     def build(self):
-        self._patch_sources()
         cmake = CMake(self)
         cmake.configure()
         cmake.build()
diff --git a/recipes/openblas/all/test_package/CMakeLists.txt b/recipes/openblas/all/test_package/CMakeLists.txt
index eaf07820c3b1c..fed4c938681b1 100644
--- a/recipes/openblas/all/test_package/CMakeLists.txt
+++ b/recipes/openblas/all/test_package/CMakeLists.txt
@@ -1,4 +1,4 @@
-cmake_minimum_required(VERSION 3.1)
+cmake_minimum_required(VERSION 3.15)
 project(test_package)
 
 find_package(OpenBLAS REQUIRED CONFIG)
diff --git a/recipes/openblas/all/test_package/conanfile.py b/recipes/openblas/all/test_package/conanfile.py
index 02eb5ce439fb4..f789a1a96acfa 100644
--- a/recipes/openblas/all/test_package/conanfile.py
+++ b/recipes/openblas/all/test_package/conanfile.py
@@ -4,11 +4,9 @@
 import os
 
 
-# It will become the standard on Conan 2.x
 class TestPackageConan(ConanFile):
     settings = "os", "arch", "compiler", "build_type"
-    generators = "CMakeDeps", "CMakeToolchain", "VirtualRunEnv"
-    test_type = "explicit"
+    generators = "CMakeDeps", "CMakeToolchain"
 
     def requirements(self):
         self.requires(self.tested_reference_str)
diff --git a/recipes/openblas/config.yml b/recipes/openblas/config.yml
index e0f3014a9fdda..a9986f1c97c73 100644
--- a/recipes/openblas/config.yml
+++ b/recipes/openblas/config.yml
@@ -1,4 +1,6 @@
 versions:
+  "0.3.28":
+    folder: all
   "0.3.27":
     folder: all
   "0.3.26":
@@ -9,13 +11,3 @@ versions:
     folder: all
   "0.3.20":
     folder: all
-  "0.3.17":
-    folder: all
-  "0.3.15":
-    folder: all
-  "0.3.13":
-    folder: all
-  "0.3.12":
-    folder: all
-  "0.3.10":
-    folder: all