70 (number)

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

70 is the fourth discrete sphenic number, as the first of the form

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.

[b] 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.

[7] For both 7 and 70, there is 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.

[8] 70 = 2 × 5 × 7 simplifies to 7 × 10, or the product of the first happy prime in decimal, and the base (10).

The sum 43 + 50 + 40 = 133 represents the one-hundredth composite number,[9] where the sum of all members in this aliquot sequence up to 70 is the fifty-ninth prime, 277 (this prime index value represents the seventeenth prime number and seventh super-prime, 59).

[10][5][c] 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.

70 is the fourth central binomial coefficient, preceding

[17] 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:

The 7-simplex can be constructed as the join of a point and a 6-simplex, whose order is 7!, where the 6-simplex has a total of seventy three-dimensional and two-dimensional elements (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.

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.

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.