# 353 (number)

 ← 352 353 354 →
Cardinal three hundred fifty-three
Ordinal 353rd
(three hundred fifty-third)
Factorization prime
Prime yes
Roman numeral CCCLIII
Binary 1011000012
Ternary 1110023
Quaternary 112014
Quinary 24035
Senary 13456
Octal 5418
Duodecimal 25512
Vigesimal HD20
Base 36 9T36

353 is the natural number between 352 and 354. It is a prime number.

## In mathematics

In connection with Euler's sum of powers conjecture, 353 is the smallest number whose 4th power is equal to the sum of four other 4th powers, as discovered by R. Norrie in 1911:[1][2][3]

${\displaystyle 353^{4}=30^{4}+120^{4}+272^{4}+315^{4}.}$

353 is a palindromic prime,[4] an irregular prime,[5] and a super-prime.[6] 353 is one of the solutions to the stamp folding problem: there are exactly 353 ways to fold a strip of eight blank stamps into a single flat pile of stamps.[7] In a seven-team round robin tournament, there are 353 combinatorially distinct outcomes in which no subset of teams wins all its games against the teams outside the subset; mathematically, there are 353 strongly connected tournaments on seven nodes.[8]

## Other uses

353 is also the country code for telephone numbers in the Republic of Ireland.

## References

1. ^
2. ^ Rose, Kermit; Brudno, Simcha (1973), "More about four biquadrates equal one biquadrate", Mathematics of Computation, 27: 491–494, doi:10.2307/2005655, JSTOR 2005655, MR 0329184.
3. ^ Erdős, Paul; Dudley, Underwood (1983), "Some remarks and problems in number theory related to the work of Euler", Mathematics Magazine, 56 (5): 292–298, doi:10.2307/2690369, JSTOR 2690369, MR 720650.
4. ^ "Sloane's A002385 : Palindromic primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
5. ^ "Sloane's A000928 : Irregular primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
6. ^ "Sloane's A006450 : Primes with prime subscripts". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
7. ^
8. ^