353 (number)

Short description: Natural number

| <- 352 | 353 | 354 ->

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List of numbers — Integers

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Cardinal| three hundred fifty-three
Ordinal| 353rd
(three hundred fifty-third)
Factorization| prime
Prime| 71st
Greek numeral| ΤΝΓ´
Roman numeral| CCCLIII
Binary| 1011000012
Ternary| 1110023
Quaternary| 112014
Quinary| 24035
Senary| 13456
Octal| 5418
Duodecimal| 25512
Hexadecimal| 16116
Vigesimal| HD20
Base 36| 9T36

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

## In mathematics

353 is a palindromic prime,[1] an irregular prime,[2] and a super-prime.[3]

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:[4][5][6]

[math]\displaystyle{ 353^4=30^4+120^4+272^4+315^4. }[/math]

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.[7]

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.[8]

## References

1. ↑ Sloane, N. J. A., ed. "Sequence A002385 (Palindromic primes)". OEIS Foundation. https://oeis.org/A002385.
2. ↑ Sloane, N. J. A., ed. "Sequence A000928 (Irregular primes)". OEIS Foundation. https://oeis.org/A000928.
3. ↑ Sloane, N. J. A., ed. "Sequence A006450 (Primes with prime subscripts)". OEIS Foundation. https://oeis.org/A006450.
4. ↑ Sloane, N. J. A., ed. "Sequence A003294 (Numbers n such that n4 can be written as a sum of four positive 4th powers)". OEIS Foundation. https://oeis.org/A003294.
5. ↑ Rose, Kermit; Brudno, Simcha (1973), "More about four biquadrates equal one biquadrate", Mathematics of Computation 27 (123): 491–494, doi:10.2307/2005655 .
6. ↑ "Some remarks and problems in number theory related to the work of Euler", Mathematics Magazine 56 (5): 292–298, 1983, doi:10.2307/2690369 .
7. ↑ Sloane, N. J. A., ed. "Sequence A051337 (Number of strongly connected tournaments on n nodes)". OEIS Foundation. https://oeis.org/A051337.
8. ↑ Sloane, N. J. A., ed. "Sequence A001011 (Number of ways to fold a strip of n blank stamps)". OEIS Foundation. https://oeis.org/A001011.

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