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'''70''' is the fourth discrete [[sphenic number]], as the first of the form <math>2 \times 5 \times r</math>.<ref>{{cite web|title=Sloane's A007304 : Sphenic numbers|url=https://oeis.org/A007304|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-29}}</ref> It is the smallest [[weird number]], a natural number that is [[Abundant number|abundant]] but not [[semiperfect]],<ref>{{cite web|title=Sloane's A006037 : Weird numbers|url=https://oeis.org/A006037|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-29}}</ref> where it is also the second-smallest [[primitive abundant number]], after [[20 (number)|20]]. 70 is in equivalence with the sum between the smallest number that is the sum of ''two'' abundant numbers, and the largest that is not ([[24 (number)|24]], [[46 (number)|46]]).
 
70 is the tenth [[Erdős–Woods number]], since it is possible to find sequences of seventy consecutive integers such that each inner member shares a [[Factor (arithmetic)|factor]] with either the first or the last member.<ref>{{cite web|title=Sloane's A059756 : Erdős-Woods numbers|url=https://oeis.org/A059756|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-29}}</ref>{{efn|1=The smallest sequence of seventy consecutive integers sharing a factor with either first or last member starts at the twenty-three digit number (with decimal representation), 26214699169906862478864 = 2<sup>4</sup> × 3 × 7 × 11 × 13 × 19 × 23 × 29 × 37 × 43 × 47 × 53 × 67 × 73 × 2221, or approximately 2.62 × 10<sup>22</sup>.<ref>{{Cite OEIS |A059757 |Initial terms of smallest Erdős-Woods intervals corresponding to the terms of A059756. |access-date=2024-07-31 }}</ref> Its largest prime factor is the sixty-seventh [[super-prime]],<ref name=A006450>{{Cite OEIS |A006450 |Prime-indexed primes: primes with prime subscripts. |access-date=2024-07-31 }}</ref> where 70 lies midway between the thirteenth pair of [[sexy prime]]s ([[67 (number)|67]], [[73 (number)|73]]).<ref>{{Cite OEIS |A023201 |Primes p such that p + 6 is also prime. (Lesser of a pair of sexy primes.) |access-date=2024-07-31 }}</ref> }} It is also the sixth [[Pell number]], preceding the tenth prime number [[29 (number)|29]], in the sequence <math>\{0, 1, 2, 5, 12, 29, \ldots\}</math>.
 
70 is a [[palindromic number]] in bases 9 (77<sub>9</sub>), 13 (55<sub>13</sub>) and 34 (22<sub>34</sub>).{{efn|1=It is also a Harshad number in bases 6, 8, 9, 10, 11, 13, 14, 15 and 16. }}
 
==== FigurateHappy numbersnumber ====
 
* 70 is the seventh [[pentagonal number]].<ref>{{cite web|title=Sloane's A000326 : Pentagonal numbers|url=https://oeis.org/A000326|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-29}}</ref> ▼
70 is the thirteenth [[happy number]] in [[decimal]], where [[7]] is the first such number greater than 1 in base ten: the sum of [[Square number|squares]] of its digits eventually reduces to [[1]].<ref>{{Cite OEIS |A007770 |Happy numbers: numbers whose trajectory under iteration of sum of squares of digits map (see A003132) includes 1. |access-date=2024-07-31 }}</ref> For both 7 and 70, there is
* 70 is also the fourth 13-gonal ([[Polygonal number|tridecagonal]]) number.<ref>{{cite web|title=Sloane's A051865 : 13-gonal (or tridecagonal) numbers|url=https://oeis.org/A051865|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-29}}</ref>▼
 
*70 is the fifth [[pentatope number]].▼
:<math>49 \mapsto 16 + 81 \mapsto 97 \mapsto 81 + 49 \mapsto 130 \mapsto 1 + 9 \mapsto 10 \mapsto 1.</math>
 
[[97 (number)|97]], which reduces from the sum of squares of digits of 49, is the only prime after 7 in the successive sums of squares of digits (7, 49, '''97''', 130, 10) before reducing to 1. More specifically, 97 is also the seventh [[happy prime]] in base ten.<ref>{{Cite OEIS |A035497 |Happy primes: primes that eventually reach 1 under iteration of "x -> sum of squares of digits of x". |access-date=2024-07-31 }}</ref>
 
70 = [[2]] × [[5]] × 7 simplifies to 7 × [[10]], or the product of the first happy prime in decimal, and the base (10).
The sum of the first seven prime numbers aside from [[7]] (i.e., 2, 3, 5, 11, …, 19) is 70; the first four primes in this sequence sum to 21 = 3 × 7, where the sum of the sixth, seventh and eighth [[Sequence|indexed]] primes (in the [[List of prime numbers|sequence of prime numbers]]) 13 + 17 + 19 is the seventh [[square number]], [[49 (number)|49]].{{efn|1=70 is the thirteenth [[happy number]] in [[decimal]], where [[7]] is the first such number greater than 1 in base ten: the sum of squares of its digits eventually reduces to [[1]].<ref>{{Cite OEIS |A007770 |Happy numbers: numbers whose trajectory under iteration of sum of squares of digits map (see A003132) includes 1. |access-date=2024-07-31 }}</ref> For 7, there is 49 ↦ 16 + 81 ↦ 97 ↦ 81 + 49 ↦ 130 ↦ 1 + 9 ↦ 10 ↦ 1. 97, in this sequence, is also more specifically the seventh [[happy prime]] in base ten.<ref>{{Cite OEIS |A035497 |Happy primes: primes that eventually reach 1 under iteration of "x -> sum of squares of digits of x". |access-date=2024-07-31 }}</ref> }}
 
==== Aliquot sequence ====
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* The composite index of 100 is 74 (the aliquot part of 70),<ref name="A002808" /> the third non-trivial member of the 43-aliquot tree.
 
The sum 43 + 50 + 40 = [[133 (number)|133]] represents the one-hundredth composite number,<ref name="A002808" /> where the sum of all members in this aliquot sequence up to 70 is the fortyfifty-ninth prime, [[277 (number)|277]] (this prime index value represents the seventeenth prime number and seventh super-prime, [[59 (number)|59]]).<ref>{{Cite OEIS |A000040 |The prime numbers. |access-date=2024-07-31 }}</ref><ref name="A006450" />{{efn|1=Meanwhile, the [[aliquot sum]] of [[164 (number)|164]] = 74 + 40 + 50 is [[130 (number)|130]],<ref>{{Cite OEIS |A001065 |Sum of proper divisors (or aliquot parts) of n: sum of divisors of n that are less than n. |access-date=2024-07-31 }}</ref> with a [[Divisor function|sum-of-divisor]]s of [[294 (number)|294]],<ref>{{Cite OEIS |A000203 |...the sum of the divisors of n. |access-date=2024-07-31 }}</ref> and an [[Arithmetic number|arithmetic mean of divisors]] of '''49'''.<ref>{{Cite OEIS |A003601 |Numbers n such that the average of the divisors of n is an integer: sigma_0(n) divides sigma_1(n). |access-date=2024-07-31 }}</ref><ref>{{Cite OEIS |A102187 |Arithmetic means of divisors of arithmetic numbers (arithmetic numbers, A003601, are those for which the average of the divisors is an integer). |access-date=2024-07-31 }}</ref> }}
 
==== CentralFigurate binomial coefficientnumbers ====
▲* 70 is the seventh [[pentagonal number]].<ref>{{cite web|title=Sloane's A000326 : Pentagonal numbers|url=https://oeis.org/A000326|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-29}}</ref>
▲* 70 is also the fourth 13-gonal ([[Polygonal number|tridecagonal]]) number.<ref>{{cite web|title=Sloane's A051865 : 13-gonal (or tridecagonal) numbers|url=https://oeis.org/A051865|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-29}}</ref>
▲*70 is the fifth [[pentatope number]].
 
The sum of the first seven prime numbers aside from [[7]] (i.e., 2, 3, 5, 11, …, 19) is 70; the first four primes in this sequence sum to 21 = 3 × 7, where the sum of the sixth, seventh and eighth [[Sequence|indexed]] primes (in the [[List of prime numbers|sequence of prime numbers]]) 13 + 17 + 19 is the seventh [[square number]], [[49 (number)|49]].
 
==== Central binomial coefficient ====
70 is the fourth [[central binomial coefficient]], preceding <math>\{1, 2, 6, 20\}</math>, as the number of ways to choose 4 objects out of 8 if order does not matter; this is in equivalence with the number of possible values of an 8-bit [[binary number]] for which half the [[bit]]s are on, and half are off.<ref>{{Cite OEIS |A000984 |Central binomial coefficients: binomial(2*n,n) as (2*n)!/(n!)^2. }}</ref>
 
=== Geometric properties ===
 
==== 7-simplex ====
[[File:7-simplex t0.svg|left|thumb|Two-dimensional orthographic projection of the [[7-simplex]], a [[uniform 7-polytope]] with seventy [[Regular tetrahedron|tetrahedral cells]] ]]
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<math>\begin{bmatrix}\begin{matrix}8 & 7 & 21 & 35 & 35 & 21 & 7 \\ 2 & 28 & 6 & 15 & 20 & 15 & 6 \\ 3 & 3 & 56 & 5 & 10 & 10 & 5 \\ 4 & 6 & 4 & 70 & 4 & 6 & 4 \\ 5 & 10 & 10 & 5 & 56 & 3 & 3 \\ 6 & 15 & 20 & 15 & 6 & 28 & 2 \\ 7 & 21 & 35 & 35 & 21 & 7 & 8 \end{matrix}\end{bmatrix}</math>
 
Aside from the 7-simplex, there are a total of seventy other [[uniform 7-polytope]]s with <math>\mathrm {A_7}</math> [[A7 polytope|symmetry]]. Worth mentioning, theThe 7-simplex can be constructed as the [[Join (topology)|join]] of a [[Point (geometry)|point]] and a [[6-simplex]], whose [[Group order|order]] is 7!., Thewhere the 6-simplex, in particular, has a total of seventy three-dimensional and two-dimensional [[Simplex#Elements|elements]] (where there are thirty-five [[3-simplex]] cells, and thirty-five [[Face (geometry)|faces]] that are [[Equilateral triangle|triangular]]).
 
70 is also the fifth [[pentatope number]], as the number of 3-dimensional unit spheres which can be packed into a [[4-simplex]] (or four-dimensional analogue of the [[regular tetrahedron]]) of edge-length 5.<ref>{{cite web|title=Sloane's A000332 : Binomial coefficient binomial(n,4) = n*(n-1)*(n-2)*(n-3)/24|url=https://oeis.org/A000332|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-29}}</ref>
 
==== Leech lattice ====
 
The sum of the first 24 squares starting from 1 is 70{{sup|2}} = 4900, i.e. a [[square pyramidal number]]. This is the only non trivial solution to the [[cannonball problem]], and relates 70 to the [[Leech lattice]] in twenty-four dimensions and thus [[string theory]].
 
== In science ==
*70 is the [[atomic number]] of [[ytterbium]], a [[lanthanide]].
 
===Astronomy= In religion ==
*[[Messier object]] [[Messier 70|M70]], a [[visual magnitude|magnitude]] 9.0 [[globular cluster]] in the [[constellation]] [[Sagittarius (constellation)|Sagittarius]]
*The [[New General Catalogue]] object [[NGC 70]], a magnitude 13.4 [[spiral galaxy]] in the constellation [[Andromeda (constellation)|Andromeda]]
 
==In religion==
* In [[Judaism|Jewish]] tradition:
** Seventy souls went down to Egypt to begin the Hebrews' Egyptian exile ({{Bibleverse||Genesis|46:27}}).
** There is a core of 70 nations and 70 world languages, paralleling the 70 names in the [[Table of Nations]].
** There were 70 men in the Great [[Sanhedrin]], the Supreme Court of ancient Israel. (Sanhedrin [http://www.mechon-mamre.org/i/e101.htm#4 1:4].)
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** {{Bibleverse||Psalm|90:10}} allots three score and ten (70 years) for a man's life, and the [[Mishnah]] attributes that age to "strength" (Avot [http://www.chaver.com/Mishnah-New/Hebrew/Text/Seder%20Nezikin/Masechet%20Avot/Masechet%20Avot%20Perek%205.htm 5:32]), as one who survives that age is described by the verse as "the strong".
**[[Ptolemy II Philadelphus]] ordered 72 Jewish elders to translate the [[Torah]] into [[Greek language|Greek]]; the result was the [[Septuagint]] (from the [[Latin language|Latin]] for "seventy"). The Roman numeral seventy, LXX, is the scholarly symbol for the Septuagint.
 
* In [[Christianity]]:
**In {{Bibleverse||Matthew|18:21-22}}, [[Jesus]] tells [[Saint Peter|Peter]] to forgive people seventy times seven times.
**In {{Bibleverse||Luke|10:1-24}}, Jesus appoints [[Seventy Disciples]] and sends them out in pairs to preach the Gospel.
*[[Seventy (Latter Day Saints)|Seventy]] is a priesthood office in the [[Latter Day Saint movement|Latter Day Saint religion]].
 
* In Islamic history and in Islamic interpretation the number 70 or 72 is most often and generally hyperbole for an infinite amount:
** There are 70 dead among the Prophet [[Muhammad]]'s adversaries during the [[Battle of Badr]].
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** In [[Shia Islam]], there are 70 martyrs among [[Imam Hussein]]'s followers during the [[Battle of Karbala]].
 
== In law ==
*In certain cases, [[Public domain#Expiration of copyright|copyrights expire]] after 70 (or 50) years, especially after the death of the latest author (see, [[Berne Convention]]).
 
== In sportsother fields ==
* In some traditions, 70 years of marriage is marked by a [[platinum]] [[wedding anniversary]].▼
*In Olympic [[archery]], the targets are 70 meters from the archers.
* Under [[Social Security (United States)]], the age at which a person can receive the maximum retirement benefits (and may do so and continue working without reduction of benefits).▼
*In [[college football]], two teams scored 70 points in bowl games, the most in such contests: first the [[2012 West Virginia Mountaineers football team|West Virginia Mountaineers]] against the [[2012 Clemson Tigers football team|Clemson Tigers]] in the [[2012 Orange Bowl]], and the [[2018 Army Black Knights football team|Army Black Knights]] against the [[2018 Houston Cougars football team|Houston Cougars]] in the [[2018 Armed Forces Bowl]].
* The number of the laps of the [[Canadian Grand Prix]] and [[Hungarian Grand Prix]].
 
==In otherNumber name fields==
{{Main article|numberNumeral name(linguistics)}}▼
{{See also|List of highways numbered 70}}
{{Wiktionary|seventy}}▼
* 70 [[miles per hour]] is a common [[speed limit]] for freeways in many [[United States|American]] states, primarily in the central United States (in the Eastern U.S. the speed limit is generally 65, in the Western U.S. it is 75).
* 70 miles per hour is the [[national speed limit]] in the [[United Kingdom]] for cars and motorcycles on the best grades of road.<ref>''The Official Highway Code'', pub. Department for Transport (Revised 2007 Edition). {{ISBN|978-0-11-552814-9}}. A white circular sign with a black diagonal stripe indicates that the national speed limit applies. This depends on the vehicle type and grade of road. The table on p. 40 shows the highest speed permitted to be 70&nbsp;mph, for normally-laden cars and motorcycles on dual-carriageways and motorways.</ref>
▲* 70 years of marriage is marked by a [[platinum]] [[wedding anniversary]].
* 70 is the [[hull classification symbol|hull number]] of the U.S. Navy's nuclear aircraft carrier [[USS Carl Vinson|USS ''Carl Vinson'' (CVN-70)]], named after U.S. Representative [[Carl Vinson]].
* The French department [[Haute-Saône]] is number 70.
* As a year, "70" may refer to [[70 BC]], [[AD 70]], or [[1970]].
* The number 70 is frequently referenced by the musical duo [[Boards of Canada]]: they have songs titled "Sixtyten" (''[[Music Has the Right to Children]]'', 1998) and "The Smallest Weird Number" (''[[Geogaddi]]'', 2002), and their record label is named [[Music70]].
▲*Under [[Social Security (United States)]], the age at which a person can receive the maximum retirement benefits (and may do so and continue working without reduction of benefits)
 
==Number name==
▲{{Main article|number name}}
Several languages, especially ones with [[vigesimal]] number systems, do not have a specific word for 70: for example, {{Lang-fr|soixante-dix|lit=sixty-ten}}; {{Lang-da|halvfjerds}}, short for {{Lang-da|halvfjerdsindstyve|lit=three and a half score|label=none}}. (For French, this is true only in France; other French-speaking regions such as [[Belgium]], [[Switzerland]], [[Aosta Valley]] and [[Jersey]] use {{Lang|fr|septante}}.<ref>Peter Higgins, ''Number Story''. London: Copernicus Books (2008): 19. "Belgian French speakers however grew tired of this and introduced the new names septante, octante, nonante etc. for these numbers".</ref>)
 
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== External links ==
▲{{Wiktionary|seventy}}
*[https://babel.hathitrust.org/cgi/pt?id=uc1.b3917316;view=1up;seq=17 On some Philological Peculiarities in the English Authorized Version of the Bible]. By Thomas Watts, Esq.
 
{{Integers|zero}}
{{Authority control}}
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