501 (number)

This article is about the number. For other uses, see 501 (disambiguation).
← 500 501 502 →
Cardinalfive hundred one
Ordinal501st
(five hundred first)
Factorization3 × 167
Greek numeralΦΑ´
Roman numeralDI
Binary1111101012
Ternary2001203
Senary21536
Octal7658
Duodecimal35912
Hexadecimal1F516

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]

  1. ^ Sloane, N. J. A. (ed.). "Sequence A007504 (Sum of first n primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^ Sloane, N. J. A. (ed.). "Sequence A051894 (Number of monic polynomials with integer coefficients of degree n with all roots in unit disc)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^ Sloane, N. J. A. (ed.). "Sequence A000247 (2^n-n-2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ^ Sloane, N. J. A. (ed.). "Sequence A000262 (Number of "sets of lists": number of partitions of {1,..,n} into any number of lists, where a list means an ordered subset)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. ^ Sloane, N. J. A. (ed.). "Sequence A069038 (G.f.: x*(1+x)^4/(1-x)^6)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  6. ^ Wolfson, Elliot R. (1997), Through a Speculum That Shines: Vision and Imagination in Medieval Jewish Mysticism, Princeton University Press, p. 222, ISBN 978-0-691-01722-8.