47 (number)

← 46 47 48 →
← 40 41 42 43 44 45 46 47 48 49 → List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	forty-seven
Ordinal	47th (forty-seventh)
Factorization	prime
Prime	15th
Divisors	1, 47
Greek numeral	ΜΖ´
Roman numeral	XLVII
Binary	1011112
Ternary	12023
Senary	1156
Octal	578
Duodecimal	3B12
Hexadecimal	2F16

47 (forty-seven) is the natural number following 46 and preceding 48. It is a prime number.

Mathematics

Forty-seven is the fifteenth prime number, a safe prime, ^[1] and the fourth isolated prime. ^[2] 47 is the number of trees on 9 unlabeled nodes. ^[3]

47 is the sixth highly cototient number, ^[4] and the eighth Eisenstein prime with no imaginary part and real part of the form ${\displaystyle 3n-1}$. ^[5]

47 is the ninth strictly non-palindromic number, following 19 and preceding 53. ^[6]

47 is the largest member of the simplest Cunningham chain, ^[7]

{2, 5, 11, 23, 47}

where each prime member is one more than twice the previous. 47 is equivalently the fifth Thabit number of the form ${\displaystyle 3\cdot 2^{n}-1}$ for positive ${\displaystyle n}$, relating to the pair of amicable numbers {17296, 18416}.

47 is the ninth Lucas number (and sixth Lucas prime), ^[8] where it is also the fourth Keith number since its digits appear as successive terms earlier in the sequence of Lucas numbers: {2, 1, 3, 4, 7, 11, 18, 29, 47, ...}. ^[9]

47 is the thirteenth supersingular prime. ^[10] It is the last consecutive prime number that divides the order of at least one sporadic group, in its case it divides the order of the two largest such (non-pariah) groups: ${\displaystyle \mathbb {M} }$ and ${\displaystyle \mathbb {B} }$. ^[11]

47 is the largest consecutive prime in Manjul Bhargava's prime-universality criterion theorem representative of all prime numbers: {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 67, 73}.

The forty-seventh triangular number (1128) is the dimensional representation of the largest vertex operator algebra with central charge of twenty-four, ${\displaystyle D_{24}}$. ^[12]

In science

47 is the atomic number of silver.

Astronomy

The 47-year cycle of Mars: after 47 years – 22 synodic periods of 780 days each – Mars returns to the same position among the stars and is in the same relationship to the Earth and Sun. The ancient Mesopotamians discovered this cycle. ^[13]

In popular culture

Pomona College

The Smith Clock Tower (right) at Pomona College has been set up to chime on the 47th minute of the hour.

The number 47 has historical implications to Pomona College, a liberal arts college in Claremont, California, and has been incorporated into various aspects of campus life. ^{[14] [15]} The tradition began in the summer of 1964, when two students, Laurie Mets and Bruce Elgin, conducted a research project seeking to find out whether the number occurs more often in nature than would be expected by chance. They documented various 47 sightings, and professor Donald Bentley produced a false mathematical proof that 47 was equal to all other integers. The number became a meme among the class, which spread once the academic year began and snowballed over time. ^[16]

Notable 47 sightings include the fact that Pomona is located off of exit 47 of Interstate 10, and the fact that the largest residential building on campus, Mudd-Blaisdell (formally Florence Carrier Blaisdell and Della Mullock Mudd Hall, a title with 47 characters), was completed in 1947 and contains a staircase with 47 balusters. ^[16]

Many Pomona alumni have deliberately inserted 47 references into their work. ^[14] Joe Menosky (class of 1979), a writer for Star Trek: The Next Generation , inserted 47 mentions into nearly every episode of the show, a practice that has been picked up by other Star Trek writers. ^{[16] [17] [18]} Pomona hosts a community service–oriented celebration every April 7 (abbreviated 4/7 in the U.S.). ^[19] In the early 2010s, the college's clock tower was set up to chime on the 47th minute of the hour. ^{[20] [21]}

Other

Late rapper Capital Steez was infatuated with the number 47 and what it meant spiritually. He believed the number 47 was the "perfect expression of balance in the world", representing the tension between the heart and the brain (the fourth and sixth chakra, respectively.) The number featured on the cover of AmeriKKKan Korruption, stylized to resemble a swastika. ^[22]

References

1. "Sloane's A005385 : Safe primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
2. Sloane, N. J. A. (ed.). "SequenceA007510(Single (or isolated or non-twin) primes: Primes p such that neither p-2 nor p+2 is prime.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-06-19.
3. "Sloane's A000055: Number of trees with n unlabeled nodes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 2010-11-29. Retrieved 2021-12-19.
4. "Sloane's A100827 : Highly cototient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
5. Sloane, N. J. A. (ed.). "SequenceA003627(Primes of the form 3n-1.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-06-19.
6. "Sloane's A016038 : Strictly non-palindromic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
7. Sloane, N. J. A. (ed.). "SequenceA075712(Rearrangement of primes into Germain groups (or Cunningham chains).)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-06-19.
8. "Sloane's A005479 : Prime Lucas numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
9. "Sloane's A007629 : Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
10. "Sloane's A002267 : The 15 supersingular primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
11. Ronan, Mark (2006). Symmetry and the Monster: One of the Greatest Quests of Mathematics . New York: Oxford University Press. pp. 244–246. ISBN   978-0-19-280722-9. MR   2215662. OCLC   180766312. Zbl   1113.00002.
12. Van Ekeren, Jethro; Lam, Ching Hung; Möller, Sven; Shimakura, Hiroki (2021). "Schellekens' list and the very strange formula". Advances in Mathematics . 380. Amsterdam: Elsevier: 1–34 (107567). arXiv: 2005.12248 . doi:10.1016/j.aim.2021.107567. MR   4200469. S2CID   218870375. Zbl   1492.17027.
13. "Astronomy 100 – Early Astronomy".
14. Lipka, Sara (11 February 2005). "Pomona's Prime Number" . The Chronicle of Higher Education . Archived from the original on October 29, 2020. Retrieved 7 April 2020.
15. "1964". Pomona College Timeline. Pomona College. Archived from the original on August 7, 2020. Retrieved 7 April 2020.
16. Dolinar, Sarah (October 1, 2000). "The Mystery of 47". Pomona College Magazine. Vol. 37, no. 1. Pomona College. Archived from the original on October 26, 2020. Retrieved 7 April 2020.
17. Shin, Daniel (September 7, 2016). "Let's do the number: 'Star Trek' and the 47 conspiracy". Marketplace . American Public Media. Archived from the original on October 1, 2020. Retrieved 7 April 2020.
18. Klein, Ezra (November 21, 2012). "The Last Word". The Last Word with Lawrence O'Donnell . NBCUniversal. 56 minutes in. MSNBC . Retrieved April 7, 2021– via Archive.org.
19. "4/7 Celebration of Sagehen Impact". Pomona College. Archived from the original on July 31, 2019. Retrieved 7 April 2019.
20. Rowan, Brendan (November 5, 2010). "Clock Tower Bell Set to Chime On the 47th Minute". The Student Life . Archived from the original on July 31, 2019. Retrieved 7 April 2019.
21. "Tower's bell ringing again at Pomona College". Los Angeles Daily News . November 7, 2010. Archived from the original on July 31, 2019. Retrieved 7 April 2019.
22. "Capital Steez: King Capital". The Fader. Rosenberg, Eli. Retrieved 2016-08-30.