35 (number) explained

Number:	35
Divisor:	1, 5, 7, 35

35 (thirty-five) is the natural number following 34 and preceding 36.

In mathematics

35 is the sum of the first five triangular numbers, making it a tetrahedral number.^[1]

35 is the 10th discrete semiprime (

5 x 7 )^[2] and the first with 5 as the lowest non-unitary factor, thus being the first of the form (5.q) where q is a higher prime.

35 has two prime factors, (5 and 7) which also form its main factor pair (5 x 7) and comprise the second twin-prime distinct semiprime pair.

The aliquot sum of 35 is 13, within an aliquot sequence of only one composite number (35,13,1,0) to the Prime in the 13-aliquot tree. 35 is the second composite number with the aliquot sum 13; the first being the cube 27.

35 is the last member of the first triple cluster of semiprimes 33, 34, 35. The second such triple distinct semiprime cluster is 85, 86, and 87.^[3]

35 is the number of ways that three things can be selected from a set of seven unique things, also known as the "combination of seven things taken three at a time".

35 is a centered cube number,^[4] a centered tetrahedral number, a pentagonal number,^[5] and a pentatope number.^[6]

35 is a highly cototient number, since there are more solutions to the equation

x - \varphi (x) = 35 than there are for any other integers below it except 1.^[7]

There are 35 free hexominoes, the polyominoes made from six squares.

Since the greatest prime factor of

35 ^{2} + 1 = 1226 is 613, which is more than 35 twice, 35 is a Størmer number.^[8]

35 is the highest number one can count to on one's fingers using senary.

35 is the number of quasigroups of order 4.

35 is the smallest composite number of the form

6 k +5 , where is a non-negative integer.

In science

• The atomic number of bromine

In other fields

• 35 mm film is the basic film gauge most commonly used for both analog photography and motion pictures.
• The minimum age of presidential candidates for election to the United States, Ireland, Poland, Russia, Trinidad and Tobago, and Uruguay.
• For Social Security in the United States, the 35 highest years of earnings are used to calculate retirement benefits.

See also

• List of highways numbered 35

Notes and References

1. Web site: Sloane's A000292 : Tetrahedral numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-05-31.
2. A001358.
3. A001748.
4. Web site: Sloane's A005898 : Centered cube numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-05-31.
5. Web site: Sloane's A000326 : Pentagonal numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-05-31.
6. Web site: Sloane's A000332 : Binomial coefficient binomial(n,4) = n*(n-1)*(n-2)*(n-3)/24. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-05-31.
7. Web site: Sloane's A100827 : Highly cototient numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-05-31.
8. Web site: Sloane's A005528 : Størmer numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-05-31.