501 (number) explained

501 (five hundred [and] one) is the natural number following 500 and preceding 502.

501 is the sum of the first eighteen primes.^[1] There are 501 degree-8 polynomials with integer coefficients, all of whose roots are in the unit disk.^[2] There are 501 ways of partitioning the digits from 0 to 9 into two sets, each of which contains at least two digits,^[3] and 501 ways of partitioning a set of five elements into any number of ordered sequences.^[4] 501 is also a figurate number based on the 5-orthoplex or 5-dimensional cross polytope.^[5]

In the gematria of Eleazar of Worms, the Hebrew words "temunah" (image) and "parsuf 'adam" (human face) both had the numerological value of 501. Eleazar used this equivalence to argue that, in several Biblical passages, God appeared to His prophets in the form of a human face.^[6]

Other uses

501 is commonly used to refer to people deported from Australia under section 501 of the 1958 Migration Act.^[7]

Notes and References

1. A007504. Sum of first n primes.
2. A051894 . Number of monic polynomials with integer coefficients of degree n with all roots in unit disc.
3. A000247 . 2^n-n-2.
4. A000262. Number of "sets of lists": number of partitions of into any number of lists, where a list means an ordered subset.
5. A069038. G.f.: x*(1+x)^4/(1-x)^6.
6. .
7. Web site: Product of Australia. Stuff. Andrea. Vance. Blair. Ensor. Iain. McGregor. 2019 . The deportees are known as 501s, named after the character section of the Australian Migration Act that allows the cancellation of their visa.