diff --git a/mysql-test/r/partition.result b/mysql-test/r/partition.result
index 7c25e948d6c..886ecb29bc7 100644
--- a/mysql-test/r/partition.result
+++ b/mysql-test/r/partition.result
@@ -1307,4 +1307,51 @@ ERROR 42000: You have an error in your SQL syntax; check the manual that corresp
 ALTER TABLE t1 ANALYZE PARTITION p1 EXTENDED;
 ERROR 42000: You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near 'EXTENDED' at line 1
 DROP TABLE t1;
+CREATE TABLE t1 (s1 BIGINT UNSIGNED)
+PARTITION BY RANGE (s1) (
+PARTITION p0 VALUES LESS THAN (0), 
+PARTITION p1 VALUES LESS THAN (1), 
+PARTITION p2 VALUES LESS THAN (18446744073709551615)
+);
+INSERT INTO t1 VALUES (0), (18446744073709551614);
+INSERT INTO t1 VALUES (18446744073709551615);
+ERROR HY000: Table has no partition for value 18446744073709551615
+DROP TABLE t1;
+CREATE TABLE t1 (s1 BIGINT UNSIGNED)
+PARTITION BY RANGE (s1) (
+PARTITION p0 VALUES LESS THAN (0),
+PARTITION p1 VALUES LESS THAN (1),
+PARTITION p2 VALUES LESS THAN (18446744073709551614),
+PARTITION p3 VALUES LESS THAN MAXVALUE
+);
+INSERT INTO t1 VALUES (-1), (0), (18446744073709551613), 
+(18446744073709551614), (18446744073709551615);
+Warnings:
+Warning	1264	Out of range value for column 's1' at row 1
+SELECT * FROM t1;
+s1
+0
+0
+18446744073709551613
+18446744073709551614
+18446744073709551615
+SELECT * FROM t1 WHERE s1 = 0;
+s1
+0
+0
+SELECT * FROM t1 WHERE s1 = 18446744073709551614;
+s1
+18446744073709551614
+SELECT * FROM t1 WHERE s1 = 18446744073709551615;
+s1
+18446744073709551615
+DROP TABLE t1;
+CREATE TABLE t1 (s1 BIGINT UNSIGNED)  
+PARTITION BY RANGE (s1) (
+PARTITION p0 VALUES LESS THAN (0),
+PARTITION p1 VALUES LESS THAN (1),
+PARTITION p2 VALUES LESS THAN (18446744073709551615),
+PARTITION p3 VALUES LESS THAN MAXVALUE
+);
+DROP TABLE t1;
 End of 5.1 tests
diff --git a/mysql-test/t/partition.test b/mysql-test/t/partition.test
index f2fed63c833..6c1e17e7cf3 100644
--- a/mysql-test/t/partition.test
+++ b/mysql-test/t/partition.test
@@ -1556,4 +1556,42 @@ ALTER TABLE t1 OPTIMIZE PARTITION p1 EXTENDED;
 ALTER TABLE t1 ANALYZE PARTITION p1 EXTENDED;
 DROP TABLE t1;
 
+#
+# Bug #29258: Partitions: search fails for maximum unsigned bigint
+#
+CREATE TABLE t1 (s1 BIGINT UNSIGNED)
+  PARTITION BY RANGE (s1) (
+  PARTITION p0 VALUES LESS THAN (0), 
+  PARTITION p1 VALUES LESS THAN (1), 
+  PARTITION p2 VALUES LESS THAN (18446744073709551615)
+);
+INSERT INTO t1 VALUES (0), (18446744073709551614);
+--error ER_NO_PARTITION_FOR_GIVEN_VALUE
+INSERT INTO t1 VALUES (18446744073709551615);
+DROP TABLE t1;
+
+CREATE TABLE t1 (s1 BIGINT UNSIGNED)
+ PARTITION BY RANGE (s1) (
+  PARTITION p0 VALUES LESS THAN (0),
+  PARTITION p1 VALUES LESS THAN (1),
+  PARTITION p2 VALUES LESS THAN (18446744073709551614),
+  PARTITION p3 VALUES LESS THAN MAXVALUE
+);
+INSERT INTO t1 VALUES (-1), (0), (18446744073709551613), 
+  (18446744073709551614), (18446744073709551615);
+SELECT * FROM t1;
+SELECT * FROM t1 WHERE s1 = 0;
+SELECT * FROM t1 WHERE s1 = 18446744073709551614;
+SELECT * FROM t1 WHERE s1 = 18446744073709551615;
+DROP TABLE t1;
+
+CREATE TABLE t1 (s1 BIGINT UNSIGNED)  
+ PARTITION BY RANGE (s1) (
+  PARTITION p0 VALUES LESS THAN (0),
+  PARTITION p1 VALUES LESS THAN (1),
+  PARTITION p2 VALUES LESS THAN (18446744073709551615),
+  PARTITION p3 VALUES LESS THAN MAXVALUE
+);
+DROP TABLE t1;
+
 --echo End of 5.1 tests
diff --git a/sql/partition_info.cc b/sql/partition_info.cc
index ab887d5dda0..67f5f48556b 100644
--- a/sql/partition_info.cc
+++ b/sql/partition_info.cc
@@ -524,6 +524,13 @@ bool partition_info::check_range_constants()
         current_largest= part_range_value;
         range_int_array[i]= part_range_value;
       }
+      else if (defined_max_value &&
+               current_largest == part_range_value &&
+               part_range_value == LONGLONG_MAX &&
+               i == (no_parts - 1))
+      {
+        range_int_array[i]= part_range_value;
+      }
       else
       {
         my_error(ER_RANGE_NOT_INCREASING_ERROR, MYF(0));
diff --git a/sql/sql_partition.cc b/sql/sql_partition.cc
index 64f96f342df..06b45e3e62a 100644
--- a/sql/sql_partition.cc
+++ b/sql/sql_partition.cc
@@ -2834,8 +2834,8 @@ int get_partition_id_range(partition_info *part_info,
       loc_part_id++;
   *part_id= (uint32)loc_part_id;
   if (loc_part_id == max_partition &&
-      range_array[loc_part_id] != LONGLONG_MAX &&
-      part_func_value >= range_array[loc_part_id])
+      part_func_value >= range_array[loc_part_id] &&
+      !part_info->defined_max_value)
     DBUG_RETURN(HA_ERR_NO_PARTITION_FOUND);
 
   DBUG_PRINT("exit",("partition: %d", *part_id));
@@ -2941,7 +2941,13 @@ uint32 get_partition_id_range_for_endpoint(partition_info *part_info,
   }
   if (left_endpoint)
   {
-    if (part_func_value >= range_array[loc_part_id])
+    longlong bound= range_array[loc_part_id];
+    /*
+      In case of PARTITION p VALUES LESS THAN MAXVALUE
+      the maximum value is in the current partition.
+    */
+    if (part_func_value > bound ||
+        (part_func_value == bound && !part_info->defined_max_value))
       loc_part_id++;
   }
   else