353 (number) explained

Number:	353
Prime:	71st

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]}

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.

353 is an index of a prime Lucas number.

Notes and References

1. Palindromic primes.
2. Irregular primes.
3. Primes with prime subscripts.
4. Web site: Chen prime. mathworld.wolfram.com.
5. Web site: Proth prime. mathworld.wolfram.com.
6. Web site: Eisentein prime. mathworld.wolfram.com.
7. Numbers n such that n⁴ can be written as a sum of four positive 4th powers.
8. .
9. .
10. Number of strongly connected tournaments on n nodes.
11. Number of ways to fold a strip of n blank stamps.