# 30 (number)

 ← 29 30 31 →
Cardinal thirty
Ordinal 30th
(thirtieth)
Numeral system trigesimal
Factorization 2 × 3 × 5
Divisors 1, 2, 3, 5, 6, 10, 15, 30
Greek numeral Λ´
Roman numeral XXX
Binary 111102
Ternary 10103
Quaternary 1324
Quinary 1105
Senary 506
Octal 368
Duodecimal 2612
Vigesimal 1A20
Base 36 U36

30 (thirty) is the natural number following 29 and preceding 31.

## In mathematics

Thirty is the sum of the first four squares, which makes it a square pyramidal number.[1]

It is a primorial[2]

30 is the smallest sphenic number, and the smallest of the form 2 × 3 × r, where r is a prime greater than 3. 30 has an aliquot sum of 42; the second sphenic number and all sphenic numbers of this form have an aliquot sum 12 greater than themselves.

Adding up some subsets of its divisors (e.g., 5, 10 and 15) gives 30, hence 30 is a semiperfect number.[3]

30 is the largest number such that all coprimes smaller than itself, except for 1, are prime.[4]

A polygon with thirty sides is called a triacontagon.

The icosahedron and the dodecahedron are Platonic solids with 30 edges. The icosidodecahedron is an Archimedean solid with 30 vertices, and the Tutte–Coxeter graph is a symmetric graph with 30 vertices.

E8 has Coxeter number 30.

Since any group G such that |G| = pnm, where p does not divide m, has a subgroup of order pn, and 30 is the only number less than 60 that is not either a prime or of the above form, it is the only candidate for the order of a simple group less than 60 that one needs other methods to reject.

Thirty is:

## History and literature

• At about age 30 (according to Luke 3:23), Jesus of Nazareth was baptized by John the Baptist, at the beginning of his public ministry of teaching and healing.
• One of the rallying-cries of the 1960s student/youth protest movement was the slogan, 'Don't trust anyone over thirty'.
• In 'The Myth of Sisyphus' the French existentialist Albert Camus comments that the age of thirty is a crucial period in the life of a man, for at that age he gains a new awareness of the meaning of time.
• In Franz Kafka's novel 'The Trial' Joseph wakes up on the morning of his thirtieth birthday to find himself under arrest for an unspecified crime. After making many futile attempts to find the nature of the crime or the name of his accuser, Joseph dies on the eve of his thirty-first birthday.
• The number of uprights that formed the Sarsen Circle at Stonehenge, also the supposed number of holes forming the arrays of Y and Z Holes at Stonehenge.
• Western Christianity's most prolific 20th century essayist, F. W. Boreham in 'Life at Thirty' ('Cliffs of Opal') mentions that in addition to Jesus commencing ministry at 30 (Luke 3:23), Joseph was 30 when he stood before Pharaoh, King of Egypt (Genesis 41:46), King David was 30 when he began to reign (2 Samuel 5:4), and the Levites were numbered from the age of 30 and upward (1 Chronicles 23:3). Also in that essay Boreham writes 'It was said of [the English poet] Keats, that "he ensphered himself in thirty perfect years and died, not young".'

## Sports

• In tennis, the number 30 represents the second point gained in a game.

## References

1. ^ "Sloane's A000330 : Square pyramidal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
2. ^ "Sloane's A002110 : Primorial numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
3. ^ "Sloane's A005835 : Pseudoperfect (or semiperfect) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
4. ^ Michael Slone, Every positive integer greater than 30 has at least one composite totative from PlanetMath. Accessed 24 April 2007
5. ^ "Sloane's A005349 : Niven (or Harshad) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
6. ^ Report of the 7 July Review Committee Accessed 18 Dec 2011