313 (number)

← 312 313 314 →
List of numbers Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	three hundred thirteen
Ordinal	313th (three hundred thirteenth)
Factorization	prime
Prime	65th, twin, palindromic
Greek numeral	ΤΙΓ´
Roman numeral	CCCXIII, cccxiii
Binary	1001110012
Ternary	1021213
Senary	12416
Octal	4718
Duodecimal	22112
Hexadecimal	13916

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

In mathematics

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]

In religion

• The number of times the word pray appears in the King James Bible.
• 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; the eschatological saviour of humankind who will appear in the end times and create a utopia.

References

1. "Sloane's A001844 : Centered square numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-02.
2. Sloane, N. J. A. (ed.). "SequenceA001913(Full reptend primes: primes with primitive root 10.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
3. Sloane, N. J. A. (ed.). "SequenceA002144(Pythagorean primes: primes of form 4*k + 1.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
4. "Sloane's A007703 : Regular primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-02.
5. Sloane, N. J. A. (ed.). "SequenceA020994(Primes that are both left-truncatable and right-truncatable.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
6. "Sloane's A007770 : Happy numbers]". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-02.
7. Sloane, N. J. A. (ed.). "SequenceA001606(Indices of prime Lucas numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
8. Razwy, Sayed Ali Asgher. A Restatement of the History of Islam & Muslims. pp. 132–133.