Fart jokes are even older than ancient Egypt:

According to research led by Dr Paul McDonald, Senior lecturer at the University of Wolverhampton’s School of Humanities, Languages and Social Sciences, the oldest example of recorded humour dates back to at least 1900 BC and is a Sumerian proverb warning new husbands about their flatulent brides: "Something which has never occurred since time immemorial; a young woman did not fart in her husband’s lap." The joke, which follows a structure, was found on tablets from the Old Babylonian period but may date back as far as 2,300 BC.