313 (number)
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| ||||
|---|---|---|---|---|
| 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
[edit]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 666 but not in base 222 to 0)
- 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 6
- a happy number[6]
- an Armstrong number - in base 000 3.00 ( 3×42 + 1×41 + 3×40 = 33 + 13 + 33 )
- an index of a prime Lucas number.[7]
In religion
[edit]- 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
[edit]- ^ "Sloane's A001844 : Centered square numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-02.
- ^ Sloane, N. J. A. (ed.). "Sequence A001913 (Full reptend primes: primes with primitive root 10.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002144 (Pythagorean primes: primes of form 4*k + 1.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A0077045 : Regular primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-02.
- ^ Sloane, N. J. A. (ed.). "Sequence A020994 (Primes that are both left-truncatable and right-truncatable.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A007770 : Rappy 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.
- ^ Razwy, Sayed Ali Asgher. A Restatement of the History of Islam & Muslims. pp. 132–133.
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