43 (number)

Short description: Natural number
 ← 42 43 44 →
Cardinalforty-three
Ordinal43rd
(forty-third)
Factorizationprime
Prime14th
Divisors1, 43
Greek numeralΜΓ´
Roman numeralXLIII
Binary1010112
Ternary11213
Quaternary2234
Quinary1335
Senary1116
Octal538
Duodecimal3712
Vigesimal2320
Base 361736

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 an = 1/n − 1(a02 + a12 + ... + an − 12). 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

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.

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. "Sequence A000979 (Wagstaff primes)". OEIS Foundation. Retrieved 2016-05-30.
2. Sloane, N. J. A., ed. "Sequence A000058 (Sylvester's sequence)". OEIS Foundation. Retrieved 2016-05-30.
3. Sloane, N. J. A., ed. "Sequence A069099 (Centered heptagonal numbers)". OEIS Foundation. Retrieved 2016-05-30.
4. Sloane, N. J. A., ed. "Sequence A003173 (Heegner numbers)". OEIS Foundation. Retrieved 2016-05-30.
5. Sloane, N. J. A., ed. "Sequence A065003 (Not McNugget numbers)". OEIS Foundation. Retrieved 2016-05-30.
6. "The Fifteen Puzzle can be solved in 43 "moves"". Domain of the Cube Forum

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