34

← 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
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 biprime and has four divisors including unity and itself. Its neighbors, 33 and 35 also are distinct biprimes 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 biprime, being within; 33,34,35, the next such cluster of biprimes 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

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 answer to the equation φ(x) = 34, making 34 a nontotient. Nor is there an answer 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 4 and ended on 384 BC February 9. 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 2 and ended on 335 BC June 19. The duration of Saros series 34 was 1298.1 years, and it contained 73 lunar eclipses.

In sports

• In baseball:
  • The number has been retired by the following teams:
    • The Minnesota Twins in honor of Kirby Puckett.
    • The Houston Astros and Texas Rangers in honor of Nolan Ryan.
    • The Oakland Athletics and Milwaukee Brewers in honor of Rollie Fingers.
  • The number was also that of Angels starting pitcher Nick Adenhart, who died on a hit and run accident on April 9, 2009.
• In basketball:
  • The number retired by the Houston Rockets in honor of its most famous wearer, Hakeem Olajuwon.
  • Boston Celtics small forward Paul Pierce wears number 34
  • The number worn by Shaquille O'Neal during his run with the Los Angeles Lakers.
• In American football:
  • The number retired by the Chicago Bears in honor of Walter Payton.
  • The number retired by the Houston Oilers/Tennessee Titans in honor of Earl Campbell
• Kevin Schwantz's race number

In other fields

34 is also:

• The traffic code of Istanbul, Turkey
• "#34," a song by Dave Matthews Band
• The magic square puzzle in the 1970s 34 Skidoo
• 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 so-called "Rule 34" of the Internet states, in one of its forms, that "If it exists, there is porn of it. No exceptions."^[1][2]
• 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)]
• In the book The Count of Monte Cristo, 34 is Edmond Dantès prisoner number.

Historical years

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

References

• Prime Curios! 34 from the Prime Pages
• The Rose Labyrinth