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# 353 (number)

 ← 352 353 354 →
Cardinalthree hundred fifty-three
Ordinal353rd
(three hundred fifty-third)
Factorizationprime
Primeyes
Greek numeralΤΝΓ´
Roman numeralCCCLIII
Binary1011000012
Ternary1110023
Quaternary112014
Quinary24035
Senary13456
Octal5418
Duodecimal25512
VigesimalHD20
Base 369T36

353 (three hundred [and] fifty-three) is the natural number following 352 and preceding 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. ^ 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.
2. ^ Rose, Kermit; Brudno, Simcha (1973), "More about four biquadrates equal one biquadrate", Mathematics of Computation, 27 (123): 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, CiteSeerX 10.1.1.210.6272, doi:10.2307/2690369, JSTOR 2690369, MR 0720650.
4. ^ Sloane, N. J. A. (ed.). "Sequence A002385 (Palindromic primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
5. ^ Sloane, N. J. A. (ed.). "Sequence A000928 (Irregular primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
6. ^ Sloane, N. J. A. (ed.). "Sequence A006450 (Primes with prime subscripts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
7. ^ 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.
8. ^