888 (number)

For other uses, see 888 (disambiguation).

← 887 888 889 →
List of numbers Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	eight hundred eighty-eight
Ordinal	888th (eight hundred eighty-eighth)
Factorization	23 × 3 × 37
Greek numeral	ΩΠΗ´
Roman numeral	DCCCLXXXVIII
Binary	11011110002
Ternary	10122203
Senary	40406
Octal	15708
Duodecimal	62012
Hexadecimal	37816

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

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

${\displaystyle 888=24\times 37.}$

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:

• 888 trees with four unlabeled and three labeled nodes, ^[4]
• 888 seven-node undirected graphs without isolated vertices, ^[5] and
• 888 non-alternating knots whose crossing number is 12. ^[6]

Crystagon

888 is also the 16th area of a crystagon, equivalent with the quotient of binomial coefficient ${\displaystyle \mathrm {C} (7n,2)}$ and ${\displaystyle 7}$ with ${\displaystyle n=16}$. ^{[7] [8]}

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

• the sum of second pentagonal numbers and hexagonal numbers (392 + 496),
• the sum of twice pentagonal numbers and triangular numbers (752 + 136), as well as
• the difference between even squares and triangular numbers (1024 − 136).

Heronian tetrahedron

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) ^{[lower-alpha 1]} with four congruent triangle faces (this primitive Heronian tetrahedron is a tetrahedron where four edges share no common factor). ^[18]

Decimal properties

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:

${\displaystyle 888\mapsto 64+64+64=192\mapsto 1+81+4=86\mapsto 64+36=100\mapsto 1.}$

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

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

• 888 (disambiguation)

Notes

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

1. Sloane, N. J. A. (ed.). "SequenceA010785(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.). "SequenceA007850(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.). "SequenceA000269(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.). "SequenceA002494(Number of n-node graphs without isolated nodes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
6. Sloane, N. J. A. (ed.). "SequenceA051763(Number of nonalternating knots with n crossings)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
7. Sloane, N. J. A. (ed.). "SequenceA022264(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.). "SequenceA272388(Longest side of Heronian tetrahedron.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-03-09.
10. Sloane, N. J. A. (ed.). "SequenceA000040(The composite numbers.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-03-09.
11. Sloane, N. J. A. (ed.). "SequenceA001065(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.). "SequenceA000203(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.). "SequenceA000010(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.). "SequenceA000396(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.). "SequenceA006316(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.). "SequenceA272390(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.). "SequenceA051004(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.). "SequenceA002998(Smallest multiple of n whose digits sum to n)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
21. Sloane, N. J. A. (ed.). "SequenceA052071(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 .
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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 .