353 (number)

Not to be confused with 353 AD or 353 BC.

Natural number

| <- 352  | 353 |  354 ->

|
|

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* 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
Senary| 13456
Octal| 5418
Duodecimal| 25512
Hexadecimal| 16116

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

## In mathematics

[edit]

353 is the 71st prime number, a palindromic prime,[1] an irregular prime,[2] a super-prime,[3] a Chen prime,[4] a Proth prime,[5] and an Eisenstein prime.[6]

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:[7][8][9]

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

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.[10]

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.[11]

353 in Mertens Function returns 0.[12]

353 is an index of a prime Lucas number.[13]

## References

[edit]

1. ^ Sloane, N. J. A. (ed.). "Sequence A002385 (Palindromic primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
2. ^ Sloane, N. J. A. (ed.). "Sequence A000928 (Irregular primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
3. ^ Sloane, N. J. A. (ed.). "Sequence A006450 (Primes with prime subscripts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
4. ^ "Chen prime". mathworld.wolfram.com.
5. ^ "Proth prime". mathworld.wolfram.com.
6. ^ "Eisentein prime". mathworld.wolfram.com.
7. ^ Sloane, N. J. A. (ed.). "Sequence A003294 (Numbers n such that n4 can be written as a sum of four positive 4th powers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
8. ^ 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.
9. ^ 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.
10. ^ Sloane, N. J. A. (ed.). "Sequence A051337 (Number of strongly connected tournaments on n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
11. ^ 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.
12. ^ Sloane, N. J. A. (ed.). "Sequence A028442 (Numbers k such that Mertens's function M(k) (A002321) is zero)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
13. ^ Sloane, N. J. A. (ed.). "Sequence A001606 (Indices of prime Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

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