313 is:

• the 65th prime number
• a twin prime with 311
• a centered square number^[1]
• a full reptend prime^[2] (and the smallest number which is a full reptend prime in base 10 but not in base 2 to 9)
• a Pythagorean prime^[3]
• a regular prime^[4]
• a palindromic prime in both decimal and binary.
• a truncatable prime^[5]
• a weakly prime in base 5
• a happy number^[6]
• an Armstrong number - in base 4 ( 3×4² + 1×4¹ + 3×4⁰ = 3³ + 1³ + 3³ )
• an index of a prime Lucas number.^[7]

• The number of soldiers that Muhammad had with him in the first battle fought by the Muslims, the Battle of Badr.^[8]
• In Twelver Shia Islam, 313 is the number of soldiers or generals that will be in the army of the 12th "Imam of time" (Mahdi).

• The number 313 is the U.S. telephone area code for the city of Detroit and nearby locales.^[9]
• Frame 313 of the Zapruder film shows the moment of impact for the bullet that killed President John F. Kennedy.^[10]
• Donald Duck's car plate bears the number 313.
• Flight 313 was a 2014 thriller movie about airline cover up.
• The sixth track of the album Get Some (album) by Snot (band) is called 313.
• The fifth track of the album Infinite (album) by Eminem is called 313.

• The year 313 AD
• The year 313 BC