According to the search results, October 13th, 2023 is a Friday and there are several observances and holidays on this day. Here are some of the events that are happening on this day:

• National Train Your Brain Day: This day encourages people to keep their brains sharp and improve their minds through healthy habits such as doing crossword puzzles, studying a foreign language, or trying logic puzzles.

• National No Bra Day: This day is observed to raise awareness about breast cancer and to encourage women to go braless for the day.

• World Egg Day: This day is celebrated to raise awareness about the nutritional value of eggs and their importance in human diets.

• National Yorkshire Pudding Day: This day celebrates the traditional British dish of Yorkshire pudding.

• National Metastatic Breast Cancer Awareness Day: This day focuses on raising awareness about metastatic breast cancer, which is a type of breast cancer that has spread to other parts of the body.

In addition to these observances, there are also some historical events and news stories that happened on October 13th, 2023, such as the Israel-Hamas war protests, anti-Israel protests in many cities across the Middle East, and the United States National Oceanic and Atmospheric Administration reporting a 99% likelihood of 2023 becoming the warmest year on record.