Natural number
353 (three hundred [and] fifty-three ) is thenatural number following352 and preceding354 . It is aprime number .
353 is the 71st prime number, apalindromic prime ,[ 1] irregular prime ,[ 2] super-prime ,[ 3] Chen prime ,[ 4] Proth prime ,[ 5] Eisenstein prime .[ 6]
In connection withEuler's sum of powers conjecture , 353 is the smallest number whose 4thpower is equal to the sum of four other4th 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-teamround 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 353strongly connected tournaments on seven nodes.[ 10]
353 is one of the solutions to thestamp folding problem : there are exactly 353 ways to fold a strip of eight blank stamps into a single flat pile of stamps.[ 11]
353 inMertens Function returns 0.[ 12]
353 is anindex of aprime Lucas number .[ 13]
353 is the international calling code forRepublic of Ireland .
^ Sloane, N. J. A. (ed.)."Sequence A002385 (Palindromic primes)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Sloane, N. J. A. (ed.)."Sequence A000928 (Irregular primes)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Sloane, N. J. A. (ed.)."Sequence A006450 (Primes with prime subscripts)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ "Chen prime" .mathworld.wolfram.com .^ "Proth prime" .mathworld.wolfram.com .^ "Eisentein prime" .mathworld.wolfram.com .^ Sloane, N. J. A. (ed.)."Sequence A003294 (Numbers n such that n4 can be written as a sum of four positive 4th powers)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ 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 ^ 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 ^ Sloane, N. J. A. (ed.)."Sequence A051337 (Number of strongly connected tournaments on n nodes)" .TheOn-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)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Sloane, N. J. A. (ed.)."Sequence A028442 (Numbers k such that Mertens's function M(k) (A002321) is zero)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Sloane, N. J. A. (ed.)."Sequence A001606 (Indices of prime Lucas numbers)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.
400 to 999
400s, 500s, and 600s 700s, 800s, and 900s
1000s and 10,000s
1000s 10,000s
100,000s to 10,000,000,000,000s
100,000 1,000,000 10,000,000 100,000,000 1,000,000,000 10,000,000,000 100,000,000,000 1,000,000,000,000 10,000,000,000,000
