43 (number)

← 42 43 44 →
← 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-three
Ordinal	43rd (forty-third)
Factorization	prime
Prime	14th
Divisors	1, 43
Greek numeral	ΜΓ´
Roman numeral	XLIII
Binary	1010112
Ternary	11213
Senary	1116
Octal	538
Duodecimal	3712
Hexadecimal	2B16

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. ^[1]

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

43 is a centered heptagonal number. ^[3]

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. ^[4]

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. ^[5]

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

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

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). ^[6]

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 non-negative whole number that is not mentioned in the Bible. ^[7]

Mysticism

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

43 is the number of triangles inside the Sri Yantra.

Notes

1. Sloane, N. J. A. (ed.). "SequenceA000979(Wagstaff primes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-05-30.
2. Sloane, N. J. A. (ed.). "SequenceA000058(Sylvester's sequence)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-05-30.
3. Sloane, N. J. A. (ed.). "SequenceA069099(Centered heptagonal numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-05-30.
4. Sloane, N. J. A. (ed.). "SequenceA003173(Heegner numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-05-30.
5. Sloane, N. J. A. (ed.). "SequenceA065003(Not McNugget numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-05-30.
6. "The Fifteen Puzzle can be solved in 43 "moves"". Domain of the Cube Forum
7. "43, 44, 45, 46, 47, 48 & 49: The Importance of Numbers in the Bible". Blog on Gants Hill United Reformed Church.

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. MR 2590266 Zbl   1263.00002