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

Last updated June 09, 2025

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

In mathematics

313 is:

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]
a palindromic number in base 2 (100111001)

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]

References

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

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[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.

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313 (number)

Contents

In mathematics

In religion

References