1. Day of the Dead: October 31 is the eve of the Day of the Dead celebration, which is a significant holiday in New Mexico. Families remember their loved ones who have passed away by making altars and offering traditional foods and beverages. Many New Mexico communities, including Albuquerque and Santa Fe, hold vibrant Day of the Dead festivals.

2. Statehood: On October 31, 1911, New Mexico achieved statehood, becoming the 47th state in the United States. The celebration was held in Santa Fe, and President William Howard Taft signed the New Mexico statehood bill into law.

3. Atomic Bomb: On October 31, 1950, the first atomic bomb exploded in New Mexico. The test, code-named "Trinity," took place at the Alamogordo test range, about 125 miles south of Albuquerque. This event marked a turning point in world history, as the atomic bomb was later used against Japan, leading to the end of World War II.

4. Roswell Incident: On October 31, 1955, a man named Joe Simonton claimed that he had been visited by aliens in Eagle River, Wisconsin, who had provided him with pancakes. While this may seem like a strange event, it is significant to New Mexico because it is often associated with the infamous Roswell UFO incident, which occurred in 1947.

5. Balloon Fiesta: The Albuquerque International Balloon Fiesta is a world-renowned event that takes place every October, usually starting on the first weekend of the month. While the festival runs for several days, the most famous day is often October 31, which includes the "Mass Ascension," where hundreds of hot air balloons take off simultaneously. This event draws thousands of visitors from around the world and has become a staple of New Mexico culture.