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888 (number)

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For other uses, see 888 (disambiguation).
← 887 888 889 →
Cardinaleight hundred eighty-eight
Ordinal888th
(eight hundred eighty-eighth)
Factorization23 × 3 × 37
Greek numeralΩΠΗ´
Roman numeralDCCCLXXXVIII
Binary11011110002
Ternary10122203
Senary40406
Octal15708
Duodecimal62012
Hexadecimal37816

888 (eight hundred eighty-eight) is the natural number following 887 and preceding 889.

It is a strobogrammatic number that reads the same right-side up and upside-down on a seven-segment calculator display, symbolic in various mystical traditions.

In mathematics

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888 is a base ten repdigit (a number all of whose digits are equal),[1] and

Where 37 is the 12th prime number.

888 is a practical number, meaning that every positive integer up to 888 itself may be represented as a sum of distinct divisors of 888.[2]

888 is equal to the sum of the first two Giuga numbers: 30 + 858 = 888.[3]

There are exactly:

Crystagon

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888 is also the 16th area of a crystagon, equivalent with the quotient of binomial coefficient and with .[7][8]

This property permits 888 to be equivalent with:[7]

Heronian tetrahedron

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888 is the 42nd longest side of a Heronian tetrahedron,[9] whose edge lengths, face areas and volumes are all integers; more specifically it is the second-largest longest side of a primitive Heronian tetrahedron (after 203, and preceding 1804)[a] with four congruent triangle faces (this primitive Heronian tetrahedron is a tetrahedron where four edges share no common factor).[18]

Decimal properties

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888 is the smallest multiple of twenty-four divisible by all of its digits,[19] whose digit sum is also itself.[20]

It is a happy number in decimal, meaning that repeatedly summing the squares of its digits eventually leads to 1:

8883 = 700227072 is the smallest cube in which each digit occurs exactly three times,[21] and the only cube in which three distinct digits each occur three times.[22]

Symbolism and numerology

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The number 888 is often symbolised within the international labour movement to symbolise the 8-hour day. Workers protested for 8 hours work, 8 hours rest and 8 hours time to themselves.

In some Christian numerology, the number 888 represents Jesus, or sometimes more specifically Christ the Redeemer. This representation may be justified either through gematria, by counting the letter values of the Greek transliteration of Jesus' name,[23] or as an opposing value to 666, the number of the beast.[24] The numerological representation of Jesus with the number 888, as the sum of the numerical values of the letters of his name, was condemned by the Church father Irenaeus as convoluted and an act which reduced "the Lord of all things" to something alphabetical.[25]

In Chinese numerology, 888 usually means triple fortune, due to 8 (pinyin: bā) sounds like 發(pinyin: fā) of 發達 (prosperity), and triplet of it is a form of strengthening of the digit 8. On its own, the number 8 is often associated with great fortune, wealth and spiritual enlightenment. Hence, 888 is considered triple.[26] For this reason, addresses and phone numbers containing the digit sequence 888 are considered particularly lucky, and may command a premium because of it.[27]

See also

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Notes

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  1. ^ 203 is a number whose average of divisors is 60, the smallest number with twelve divisors and forty-second composite.[10] On the other hand, its aliquot sum is 37,[11] and its sum-of-divisors is 240,[12] which is in equivalence with the number of root vectors of E8 in the eighth dimension.[13] Its Euler totient is 168,[14] which is the symmetry order of the automorphism of the Fano plane in three dimensions,[15] and the product of the first two perfect numbers.[16]
    On the other hand, 1804 is a number k such that k64 + 1 is prime.[17]

References

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  1. ^ Sloane, N. J. A. (ed.). "Sequence A010785 (Repdigit numbers, or numbers with repeated digits)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^ Nombres pratiques Archived 2012-11-13 at the Wayback Machine (in French), Jeux et Mathématiques, Jean-Paul Davalan, retrieved 2013-01-31.
  3. ^ Sloane, N. J. A. (ed.). "Sequence A007850 (Giuga numbers: composite numbers n such that p divides n/p - 1 for every prime divisor p of n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-09-20.
  4. ^ Sloane, N. J. A. (ed.). "Sequence A000269 (Number of trees with n nodes, 3 of which are labeled)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. ^ Sloane, N. J. A. (ed.). "Sequence A002494 (Number of n-node graphs without isolated nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  6. ^ Sloane, N. J. A. (ed.). "Sequence A051763 (Number of nonalternating knots with n crossings)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  7. ^ a b Sloane, N. J. A. (ed.). "Sequence A022264 (a(n) equal to n*(7*n - 1)/2.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-03-31.
  8. ^ Tavares, Leo. Sloane, N. J. A. (ed.). "Illustration: Crysta-gons". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-03-31.
  9. ^ Sloane, N. J. A. (ed.). "Sequence A272388 (Longest side of Heronian tetrahedron.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-03-09.
  10. ^ Sloane, N. J. A. (ed.). "Sequence A000040 (The composite numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-03-09.
  11. ^ Sloane, N. J. A. (ed.). "Sequence A001065 (Sum of proper divisors (or aliquot parts) of n: sum of divisors of n that are less than n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-03-09.
  12. ^ Sloane, N. J. A. (ed.). "Sequence A000203 (a(n) is sigma(n), the sum of the divisors of n. Also called sigma_1(n).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-03-09.
  13. ^ Wilson, R.A. (April 2012). "An eightfold path to E8" (PDF) (Paper). Queen Mary University London. p. 8–10. S2CID 226997354
  14. ^ Sloane, N. J. A. (ed.). "Sequence A000010 (Euler totient function phi(n): count numbers less than or equal to n and prime to n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-03-09.
  15. ^ Lloyd, E. Keith (1995). "The Reaction Graph of the Fano Plane". In Ku, Tung-Hsin (ed.). Combinatorics and Graph Theory '95. Proceedings of the Summer School and International Conference on Combinatorics. Singapore: World Scientific. pp. 260–262. doi:10.1142/9789814532495. ISBN 978-9810223175. MR 1476206.
  16. ^ Sloane, N. J. A. (ed.). "Sequence A000396 (Perfect numbers k: k is equal to the sum of the proper divisors of k.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-03-09.
  17. ^ Sloane, N. J. A. (ed.). "Sequence A006316 (Numbers k such that k^64 + 1 is prime.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-03-09.
  18. ^ Sloane, N. J. A. (ed.). "Sequence A272390 (Longest side of primitive Heronian tetrahedron with 4 congruent triangle faces.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-03-09.
  19. ^ Sloane, N. J. A. (ed.). "Sequence A051004 (Numbers divisible both by their individual digits and by the sum of their digits)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  20. ^ Sloane, N. J. A. (ed.). "Sequence A002998 (Smallest multiple of n whose digits sum to n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  21. ^ Sloane, N. J. A. (ed.). "Sequence A052071 (a(n)^3 is the smallest cube whose digits occur with the same frequency n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  22. ^ Khovanova, Tanya (2008), Number Gossip (PDF), Gathering for Gardner, arXiv:0804.2277, Bibcode:2008arXiv0804.2277K, archived from the original (PDF) on 2017-12-09, retrieved 2018-05-23.
  23. ^ Dudley, Underwood (1997), Numerology: Or What Pythagoras Wrought, MAA Spectrum, Cambridge University Press, p. 105, ISBN 9780883855249.
  24. ^ Cheiro (2005), Book Of Fate And Fortune: Numerology And Astrology, Orient Paperbacks, p. 60, ISBN 9788122200461.
  25. ^ Juan Acevedo, Alphanumeric Cosmology from Greek to Arabic, Mohr Siebeck 2020 p. 159
  26. ^ Ratzan, Lee (2004), Understanding Information Systems: What They Do and Why We Need Them, American Library Association, p. 202, ISBN 9780838908686.
  27. ^ Hooker, John (2003), Working Across Cultures, Stanford University Press, p. 191, ISBN 9780804748070.
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