43 (number)

657356577
List of numbers Integers ← 100 101 102 103 104 105 106 107 108 109
Cardinal	six hundred fifty-seven million three hundred fifty-six thousand five hundred seventy-seven
Ordinal	657356577th (six hundred fifty-seven million three hundred fifty-six thousand five hundred seventy-seventh)
Factorization	1.3
Prime	30
Divisors	1.4.30
Greek numeral	${\stackrel {\digamma \epsilon \psi \lambda \epsilon }{\mathrm {M} }}$͵Ϛφοζ´
Roman numeral	N/A
Binary	1001110010111001110111001000012
Ternary	12002102210112002203
Senary	1451212332536
Octal	47134734418
Duodecimal	16419282912
Hexadecimal	272E772116

43 (forty-three) is the natural number following 42 and preceding 44.

Mathematics

Forty-three is the 14th smallest prime number. The previous is forty-one, with which it comprises a twin prime, and the next is 47. 43 is the smallest prime that is not a Chen prime. It is also the third Wagstaff prime.

43 is the fourth term of Sylvester's sequence, one more than the product of the previous terms (2 × 3 × 7).

43 is a centered heptagonal number.

Let a₀ = a₁ = 1, and thenceforth a_n = ⁠1/n − 1⁠(a₀² + a₁² + ... + a_{n − 1}²). This sequence continues 1, 1, 2, 3, 5, 10, 28, 154... (sequence A003504 in the OEIS). a₄₃ is the first term of this sequence that is not an integer.

43 is a Heegner number.

43 is the largest prime which divides the order of the Janko group J₄.

43 is a repdigit in base 6 (111).

43 is the largest natural number that is not an (original) McNugget number.

43 is the smallest prime number expressible as the sum of 2, 3, 4, or 5 different primes:

• 43 = 41 + 2
• 43 = 11 + 13 + 19
• 43 = 2 + 11 + 13 + 17
• 43 = 3 + 5 + 7 + 11 + 17.

43 is the smallest number with the property 43 = 4*prime(4) + 3*prime(3). Where prime(n) is the n-th prime number. There are only two numbers with that property, the other one is 127.

When taking the first six terms of the Taylor series for computing e, one obtains

$\sum _{i=0}^{5}{\frac {1}{i!}}={\frac {163}{60}}=2+{\frac {43}{60}},\$

which is also five minus the fifth harmonic number.

Every solvable configuration of the Fifteen puzzle can be solved in no more than 43 multi-tile moves (i.e. when moving two or three tiles at once is counted as one move).

Science

The chemical element with the atomic number 43 is technetium. It has the lowest atomic number of any element that does not possess stable isotopes.

Music

The number of notes in Harry Partch's 43-tone scale of just intonation.

Literature

• "Number 43", in Sonnets from the Portuguese (1850), is one of Elizabeth Barrett Browning's most famous poems.
• 43 is the smallest number that is not mentioned in the Bible.

Mysticism

The Sri Yantra, with nine interlocking triangles that collectively form 43 smaller triangles

43 is the number of triangles inside the Sri Yantra.

References

• Lehmer, Derrick, List of prime numbers from 1 to 10,006,721, Carnegie Institution of Washington, 1914
• Wells, David, Prime Numbers: The Most Mysterious Figures in Math, Wiley, 2005, ISBN 0-471-46234-9
• Crandall, Richard and Pomerance, Carl, Prime Numbers: A Computational Perspective, Springer, 2005, ISBN 0-387-25282-7

Further reading

Lenstra, Hendrik (2009). Ode to the number 43 (In Dutch). Nieuw Arch. Wiskd. Amsterdam, NL: Koninklijk Wiskundig Genootschap (5) 10, No. 4: 240-244. MR2590266 Zbl 1263.00002