70 (number)

← 69 70 71 →
← 70 71 72 73 74 75 76 77 78 79 → List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	seventy
Ordinal	70th (seventieth)
Factorization	2 × 5 × 7
Divisors	1, 2, 5, 7, 10, 14, 35, 70
Greek numeral	Ο´
Roman numeral	LXX
Binary	10001102
Ternary	21213
Senary	1546
Octal	1068
Duodecimal	5A12
Hexadecimal	4616
Hebrew	ע
Lao	໗
Armenian	Հ
Babylonian numeral	𒐕𒌋
Egyptian hieroglyph	𓎌

70 (seventy) is the natural number following 69 and preceding 71.

70 is the value $n$ whose factorial is closest to a googol, where $70!\approx 1.1978571\ldots \times 10^{100}$.

Mathematics

Properties of the integer

70 is the fourth discrete sphenic number, as the first of the form $2\times 5\times r$. It is the smallest weird number, a natural number that is abundant but not semiperfect, where it is also the second-smallest primitive abundant number, after 20. 70 is in equivalence with the sum between the smallest number to that is the sum of two abundant numbers, and the largest that is not (24, 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 with either the first or the last member. It is also the sixth Pell number, preceding the tenth prime number 29, in the sequence $\{0,1,2,5,12,29,\ldots \}$.

70 is a palindromic number in bases 9 (77₉), 13 (55₁₃) and 34 (22₃₄).

Figurate numbers

• 70 is the seventh pentagonal number.
• 70 is also the fourth 13-gonal (tridecagonal) number.
• 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 indexed primes (in the sequence of prime numbers) 13 + 17 + 19 is the seventh square number, 49.

Aliquot sequence

70 contains an aliquot sum of 74, in an aliquot sequence of four composite numbers (70, 74, 40, 50, 43) in the prime 43-aliquot tree.

• The composite index of 70 is 50, which is the first non-trivial member of the 43-aliquot tree.
• 40, the Euler totient of 100 (as twice 50), is the second non-trivial member of the 43-aliquot tree.
• The composite index of 100 is 74 (the aliquot part of 70), the third non-trivial member of the 43-aliquot tree.

Central binomial coefficient

70 is the fourth central binomial coefficient, preceding $\{1,2,6,20\}$, 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 bits are on, and half are off.

Geometric properties

7-simplex

Two-dimensional orthographic projection of the 7-simplex, a uniform 7-polytope with seventy tetrahedral cells

In seven dimensions, the number of tetrahedral cells in a 7-simplex is 70. This makes 70 the central element in a seven by seven matrix configuration of a 7-simplex in seven-dimensional space:

${\begin{bmatrix}{\begin{matrix}8&7&21&35&35&21&7\\2&28&6&15&20&15&6\\3&3&56&5&10&10&5\\4&6&4&70&4&6&4\\5&10&10&5&56&3&3\\6&15&20&15&6&28&2\\7&21&35&35&21&7&8\end{matrix}}\end{bmatrix}}$

Aside from the 7-simplex, there are a total of seventy other uniform 7-polytopes with $\mathrm {A_{7}}$ symmetry. Worth mentioning, the 7-simplex can be constructed as the join of a point and a 6-simplex, whose order is 7!. The 6-simplex, in particular, has a total of seventy three-dimensional and two-dimensional elements (where there are thirty-five 3-simplex cells, and thirty-five faces that are 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.

Leech lattice

The sum of the first 24 squares starting from 1 is 70² = 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

• Messier object M70, a magnitude 9.0 globular cluster in the constellation Sagittarius
• The New General Catalogue object NGC 70, a magnitude 13.4 spiral galaxy in the constellation Andromeda

In religion

• In Jewish tradition:
  • Seventy souls went down to Egypt to begin the Hebrews' Egyptian exile (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 1:4.)
  • According to the Jewish Aggada, there are 70 perspectives ("faces") to the Torah (Numbers Rabbah 13:15).
  • Seventy elders were assembled by Moses on God's command in the desert (Numbers 11:16–30).
  • Psalm 90:10 allots three score and ten (70 years) for a man's life, and the Mishnah attributes that age to "strength" (Avot 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; the result was the Septuagint (from the Latin for "seventy"). The Roman numeral seventy, LXX, is the scholarly symbol for the Septuagint.
• In Christianity:
  • In Matthew 18:21–22, Jesus tells Peter to forgive people seventy times seven times.
  • In Luke 10:1–24, Jesus appoints Seventy Disciples and sends them out in pairs to preach the Gospel.
• Seventy is a priesthood office in the 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.
  • 70 of the Prophet Muhammad's followers are martyred at the Battle of Uhud.
  • In Shia Islam, there are 70 martyrs among Imam Hussein's followers during the Battle of Karbala.

In law

• In certain cases, copyrights expire after 70 years.

In sports

• In Olympic archery, the targets are 70 meters from the archers.
• In college football, two teams scored 70 points in bowl games, the most in such contests: first the West Virginia Mountaineers against the Clemson Tigers in the 2012 Orange Bowl, and the Army Black Knights against the Houston Cougars in the 2018 Armed Forces Bowl.
• The number of the laps of the Canadian Grand Prix and Hungarian Grand Prix.

In other fields

See also: List of highways numbered 70

• 70 miles per hour is a common speed limit for freeways in many 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.
• 70 years of marriage is marked by a platinum wedding anniversary.
• 70 is the hull number of the U.S. Navy's nuclear aircraft carrier 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, French: soixante-dix, lit. 'sixty-ten'; Danish: halvfjerds, short for halvfjerdsindstyve, 'three and a half score'. (For French, this is true only in France; other French-speaking regions such as Belgium, Switzerland, Aosta Valley and Jersey use septante.)

External links

• On some Philological Peculiarities in the English Authorized Version of the Bible. By Thomas Watts, Esq.