34 (number)

← 33 35 → 34
← 30 31 32 33 34 35 36 37 38 39 → List of numbers — Integers 0 10 20 30 40 50 60 70 80 90 →
Cardinal	thirty-four
Ordinal	34th (thirty-fourth)
Factorization	$2 \cdot 17$
Divisors	1, 2, 17, 34
Roman numeral	XXXIV
Binary	1000102
Octal	428
Duodecimal	2A12
Hexadecimal	2216

34 (thirty-four) is the natural number following 33 and preceding 35.

In mathematics

34 is the ninth distinct semiprime and has four divisors including unity and itself. Its neighbors, 33 and 35 also are distinct semiprimes having four divisors each, and 34 is the smallest number to be surrounded by numbers with the same number of divisors as it has. It is also in the first cluster of three distinct semiprimes, being within 33,34,35; the next such cluster of semiprimes is 85,86,87.

It is the ninth Fibonacci number and a companion Pell number. Since it is an odd-indexed Fibonacci number, 34 is a Markov number, appearing in solutions with other Fibonacci numbers, such as (1, 13, 34), (1, 34, 89), etc.

This number is the magic constant of a 4 by 4 normal magic square:^[1]

Thirty-four is a heptagonal number.

It has the aliquot sum, 20, in the following descending sequence 34,20,22,14,10,8,7,1. and it is the 6th composite member of the 7-aliquot tree.

There is no solution to the equation φ(x) = 34, making 34 a nontotient. Nor is there a solution to the equation x - φ(x) = 34, making 34 a noncototient.

In science

• The atomic number of selenium
• Messier object M34, a magnitude 6.0 open cluster in the constellation Perseus
• The New General Catalogue object NGC 34, a peculiar galaxy in the constellation Cetus
• The Saros number of the solar eclipse series which began on 1917 BC August and ended on 384 BC February. The duration of Saros series 34 was 1532.5 years, and it contained 86 solar eclipses.
• The Saros number of the lunar eclipse series which began on 1633 BC May and ended on 335 BC June. The duration of Saros series 34 was 1298.1 years, and it contained 73 lunar eclipses.

In sports

• The jersey number 34 has been retired by several North American sports teams in honor of past playing greats or other key figures:
  • In Major League Baseball:
    • The Houston Astros and Texas Rangers, both for Hall of Famer Nolan Ryan.
    • The Minnesota Twins, for Hall of Famer Kirby Puckett.
    • The Oakland Athletics and Milwaukee Brewers, both for Hall of Famer Rollie Fingers.
    • Additionally, the Los Angeles Dodgers have not issued the number since the departure of Fernando Valenzuela following the 1990 season. Under current team policy, Valenzuela's number is not eligible for retirement because he is not in the Hall of Fame.
  • In the NBA:
    • The Houston Rockets, for Hall of Famer Hakeem Olajuwon.
  • In the NFL:
    • The Chicago Bears, for Hall of Famer Walter Payton.
    • The Houston Oilers, for Hall of Famer Earl Campbell. The franchise continues to honor the number in its current incarnation as the Tennessee Titans.

In other fields

34 is also:

• The traffic code of Istanbul, Turkey
• Rule 34 of the Internet, a meme stating that "If it exists, there is porn of it. No exceptions."^[2][3]
• Rule 34 (novel), a novel by Charles Stross^[4][5]
• "#34", a song by the Dave Matthews Band
• 34 Skidoo, the 1970s magic square puzzle
• In the title of the 1947 movie Miracle on 34th Street, remade in 1994
• The number of the French department Hérault
• +34 is the code for international direct-dial phone calls to Spain
• The lucky number of Victor Pelevin's protagonist Stepan Mikhailov in the novel Numbers, published as part of DTT(NN) [Dialectics in Times of Transition (from Nowhere into Nothing)]
• Request for production, Rule 34 of the U.S. Federal Rules of Civil Procedure.

Historical years

34 A.D., 34 B.C., 1934, 2034, etc.

References

1. ^ Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 53. ISBN 978-1-84800-000-1. 
2. ^ "Internet rules and laws: the top 10, from Godwin to Poe". The Daily Telegraph. 2009-10-23. http://www.telegraph.co.uk/technology/news/6408927/Internet-rules-and-laws-the-top-10-from-Godwin-to-Poe.html. Retrieved 2010-11-12. 
3. ^ Grossman, Lev (July 18, 2011). "The Boy Who Lived Forever". Time 178 (3): 50. 
4. ^ http://www.antipope.org/charlie/blog-static/2010/08/apropos-nothing.html
5. ^ http://www.amazon.com/Rule-34-Charles-Stross/dp/0441020348/

External links

• Prime Curios! 34 from the Prime Pages