Question: What is the name of the kingdom that followed the ancient Egypt's Fourth Dynasty?

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Helwan (cemetery): At Helwan south of modern Cairo was excavated a large Ancient Egyptian cemetery with more than 10.000 burials.  The cemetery was in use from the Naqada Period around 3200 BC to the Fourth Dynasty and again at the beginning of the Middle Kingdom and then up to the Roman Period and beyond.  The burial ground was discovered and excavated by Zaki Saad in 1942 to 1954.  Further excavations started in 1997 by an Australian expedition.  The excavations of Zaki Saad were never fully published, only several preliminary reports appeared.  Helwan was most likely the cemetery of Memphis in the first Dynasties.  The tombs range from small pits to bigger elaborated mastabas. Regarding the underground parts of these tombs, two types are attested.  There are on one side pits with the burial at the bottom and there are on the other side underground chambers, reached via a pit or via a staircase.  The majority of burials are for one deceased.  There are some examples of multiple burials.  The deceased were mostly place in reed mats or coffins of different materials.  Most of the bodies were found in a contracted position.  Most tombs were built of mud bricks.  Roofs are often made of timber.  Some walls in the underground chambers were covered with plaster.  In several tombs stones were found, used for roofing the tomb chamber, for blocking the entrance and in rare cases for paving walls.  Some of the more elaborate tombs had several underground chambers.  These chambers were often reached via a staircase.  The people buried here belonged to all levels of society, albeit the highest officials were buried at Saqqara.  Over 40 stelae were found belonging to the upper levels of society.  They are an important source for early writing in Egypt.  A certain Meriiti bears many titles on his stela and dates moast likely to the First Dynasty.  A few stelae also belong to members of the royal family, such as the "king's daughter" Satkhnum, the "king's daughter" Khenmetptah and the "king's son" Nisuheqet.  The stela date from about the middle of the First Dynasty to the early Fourth Dynasty.

Middle Kingdom of Egypt: The Middle Kingdom of Egypt (also known as The Period of Reunification) is the period in the history of ancient Egypt between circa 2050 BC and 1800 BC, stretching from the reunification of Egypt under the impulse of Mentuhotep II of the Eleventh Dynasty to the end of the Twelfth Dynasty.  Some scholars also include the Thirteenth Dynasty of Egypt wholly into this period as well, in which case the Middle Kingdom would finish c. 1650, while others only include it until Merneferre Ay c. 1700 BC, last king of this dynasty to be attested in both Upper and Lower Egypt.  During the Middle Kingdom period, Osiris became the most important deity in popular religion.

Peseshet: Peseshet, who lived under the Fourth Dynasty (albeit a date to the Fifth Dynasty is also possible), is often credited with being the earliest known female physician in ancient Egypt, though another, Merit-Ptah lived earlier.  Her relevant title was "lady overseer of the female physicians," but whether she was a physician herself is uncertain.  She also had the titles "king's acquaintance", and "overseer of funerary-priests of the king's mother".

Khafre Enthroned: Khafre Enthroned is a funerary statue of the Pharaoh Khafre, who reigned during the Fourth dynasty of ancient Egypt (c. 2570 BC).  It is now located in the Egyptian Museum in Cairo.  The construction is made of anorthosite gneiss, (related to diorite) a valuable, extremely hard, and dark stone brought 400 miles down the Nile River from royal quarries.  This highlights Khafre’s importance and power as a ruler.  The statue was carved for the Pharaoh’s valley temple near the Great Sphinx, a part of the necropolis (a funerary city) used in funeral rituals.  This Old Kingdom statue has an important function in Egyptian tombs as substitute abodes for the Pharaoh’s ka—the life force that accompanied a person with a kind of other self.  After death, the ka leaves the body into the afterlife, but still needs a place to rest: the statue.

Khufu ship: The Khufu ship is an intact full-size vessel from Ancient Egypt that was sealed into a pit in the Giza pyramid complex at the foot of the Great Pyramid of Giza around 2500 BC.  The ship now is preserved in the Giza Solar boat museum.  The ship was almost certainly built for Khufu (King Cheops), the second pharaoh of the Fourth Dynasty of the Old Kingdom of Egypt.  Like other buried Ancient Egyptian ships, it was apparently part of the extensive grave goods intended for use in the afterlife, and contained no bodies, unlike northern European ship burials.

Fourth Dynasty of Egypt: The Fourth Dynasty of ancient Egypt (notated Dynasty IV or Dynasty 4) is characterized as a "golden age" of the Old Kingdom.  Dynasty IV lasted from c. 2613 to 2494 BC.  It was a time of peace and prosperity as well as one during which trade with other countries is documented.

Mark Lehner: Mark Lehner is an American archaeologist with more than 30 years of experience excavating in Egypt.  His approach, as director of Ancient Egypt Research Associates (AERA), is to conduct interdisciplinary archaeological investigation.  Every excavated object is examined by specialists to create an overall picture of an archaeological site—from the buildings down to the pollen spores.  His international team currently runs the Giza Plateau Mapping Project, excavating and mapping the ancient city of the builders of the Giza pyramid complex, which dates to the fourth dynasty of Egypt.  He discovered that Pyramid G1-a, one of the subsidiary pyramids of the Great Pyramid, belonged to Hetepheres I; it was originally thought to belong to Queen Meritites I.

Fourth Dynasty of Egypt family tree: Family tree of the Fourth Dynasty of Egypt, ruling ancient Egypt in the 27th century BCE to the 25th century BCE.

Ancient Egypt: Ancient Egypt was a civilization of ancient Northeastern Africa, concentrated along the lower reaches of the Nile River in the place that is now the country Egypt.  It is one of six historic civilizations to arise independently.  Egyptian civilization followed prehistoric Egypt and coalesced around 3150 BC (according to conventional Egyptian chronology) with the political unification of Upper and Lower Egypt under Menes (often identified with Narmer).  The history of ancient Egypt occurred as a series of stable kingdoms, separated by periods of relative instability known as Intermediate Periods: the Old Kingdom of the Early Bronze Age, the Middle Kingdom of the Middle Bronze Age and the New Kingdom of the Late Bronze Age.

Khufu Statuette: The Khufu Statuette or the Ivory figurine of Khufu is an Ancient Egyptian statue.  Historically and archaeologically significant, it was found in 1903 by Sir William Matthew Flinders Petrie during excavation of Kom el-Sultan in Abydos, Egypt.  It depicts the Ancient Egyptian Pharaoh Khufu, a member of the Fourth dynasty (Old Kingdom), and the builder of the Great Pyramid.

Supporting paragraphs: Khufu Statuette Ancient Egypt
Answer: Middle Kingdom of the Middle Bronze Age