353 (number)

Not to be confused with 353 AD or 353 BC.

← 352 353 354 →
List of numbers Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	three hundred fifty-three
Ordinal	353rd (three hundred fifty-third)
Factorization	prime
Prime	71st
Greek numeral	ΤΝΓ´
Roman numeral	CCCLIII, 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

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]}

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

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]

In other fields

353 is the international calling code for Republic of Ireland.

References

1. Sloane, N. J. A. (ed.). "SequenceA002385(Palindromic primes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
2. Sloane, N. J. A. (ed.). "SequenceA000928(Irregular primes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
3. Sloane, N. J. A. (ed.). "SequenceA006450(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.). "SequenceA003294(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.). "SequenceA051337(Number of strongly connected tournaments on n nodes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
11. Sloane, N. J. A. (ed.). "SequenceA001011(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.). "SequenceA028442(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.). "SequenceA001606(Indices of prime Lucas numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.