From Wikipedia, the free encyclopedia
Natural number
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] a
super-prime ,
[3] a
Chen prime ,
[4] a
Proth prime ,
[5] and an
Eisentein 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
^
Sloane, N. J. A. (ed.).
"Sequence A002385 (Palindromic primes)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A000928 (Irregular primes)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A006450 (Primes with prime subscripts)" . The
On-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)" . The
On-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)" . The
On-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)" . The
On-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)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A001606 (Indices of prime Lucas numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
100,000
1,000,000
10,000,000
100,000,000
1,000,000,000