# 353 (number)

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Cardinal | three hundred fifty-three | |||

Ordinal |
353rd (three hundred fifty-third) | |||

Factorization | prime | |||

Prime | yes | |||

Greek numeral | ΤΝΓ´ | |||

Roman numeral | CCCLIII | |||

Binary |
101100001_{2} | |||

Ternary |
111002_{3} | |||

Quaternary |
11201_{4} | |||

Quinary |
2403_{5} | |||

Senary |
1345_{6} | |||

Octal |
541_{8} | |||

Duodecimal |
255_{12} | |||

Hexadecimal |
161_{16} | |||

Vigesimal |
HD_{20} | |||

Base 36 |
9T_{36} |

**353** (**three hundred [and] fifty-three**) is the natural number following 352 and preceding 354. It is a prime number.

## In mathematics[edit]

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]}

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[edit]

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

## References[edit]

**^**Sloane, N.J.A. (ed.). "Sequence A003294 (Numbers n such that n^4 can be written as a sum of four positive 4th powers)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation.**^**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.**^**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 0720650.**^**Sloane, N.J.A. (ed.). "Sequence A002385 (Palindromic primes)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation.**^**Sloane, N.J.A. (ed.). "Sequence A000928 (Irregular primes)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation.**^**Sloane, N.J.A. (ed.). "Sequence A006450 (Primes with prime subscripts)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation.**^**Sloane, N.J.A. (ed.). "Sequence A001011 (Number of ways to fold a strip of n blank stamps)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation.**^**Sloane, N.J.A. (ed.). "Sequence A051337 (Number of strongly connected tournaments on n nodes)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation.