July 9th, 2011

Cartoon Ross (Spring/Fall)

Blatantly stolen from Wikipedia

43

Forty-three is the 14th smallest prime number. The previous is forty-one, with which it comprises a twin prime, and the next is forty-seven. 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 a(0) = a(1) = 1, and thenceforth a(n) = (a(0)2 + a(1)2 + ... + a(n-1)2) / (n-1). This sequence continues 1 1 2 3 5 10 28 154... (sequence A003504 in OEIS). Amazingly, a(43) is the first term of this sequence that is not an integer.

43 is a Heegner number.

43 is a repdigit in base 6 (111).

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

This is the smallest 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.
4 15 17 7
5 19 13 6
20 9 2 12
14 0 11 18

The date magic square at right illustrates the magic constant as the sum of four primes:


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.