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313 (three hundred [and] thirteen) is the natural number following 312 and preceding 314.

Additionally, 313 is:

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

References

^ "Sloane's A001844 : Centered square numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-02.
^ "Sloane's A007703 : Regular primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-02.
^ "Sloane's A007770 : Happy numbers]". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-02.
^ Sloane, N. J. A. (ed.). "Sequence A001606 (Indices of prime Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.