353 is the 71st prime number, a
palindromic prime, an
irregular prime, a
super-prime, a
Chen prime, a
Proth prime, and an
Eisenstein prime. 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: :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. 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. 353 in
Mertens Function returns 0. 353 is an
index of a
prime Lucas number. ==In other fields==