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]

In other fields

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

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