43 is a Prime Number
43 = 12 + 3 + 4 + 5 + 6 + 7 + 8 + 9
43 = 98 − 76 + 54 − 32 − 1
43 = 0^1 − 1^8 + 2^7 − 3^9 + 4^5 + 5^6 + 6^2 + 7^4 + 8^3 + 9^0
3 = (1 + 1) × (11 + 11) − 1
= 2 × 22 − 2/2
= 3 × 3 + 33 + 3/3
= 44 − 4/4
= 55 − (55 + 5)/5
= 6 × 6 + 6 + 6/6
= 7 × 7 − 7 + 7/7
= 8 + 8 + 8 + 8 + 88/8
= 9 × 9 − 9 − 9 − 9 − 99/9
Number of fractions in Farey series of order 11: 0/1, 1/11, 1/10, 1/9, 1/8, 1/7, 1/6, 2/11, 1/5, 2/9, 1/4, 3/11, 2/7, 3/10, 1/3, 4/11, 3/8, 2/5, 3/7, 4/9, 5/11, 1/2, 6/11, 5/9, 4/7, 3/5, 5/8, 7/11, 2/3, 7/10, 5/7, 8/11, 3/4, 7/9, 4/5, 9/11, 5/6, 6/7, 7/8, 8/9, 9/10, 10/11, 1/1
43 is a twin prime of 41.
43 is the smallest prime that is not a Chen prime.
43 is also a Wagstaff prime, and a Heegner number
a(n) = (6^n - 1)/5, n = 3
43 smallest integer solution of the equation x2 - 1847*y2 = 1 , 18482 - 1847*432 = 1
Prime of the form k^2 + k + 41
\( \exp{ \pi \sqrt{43}} \approx 960^3 + 744 \)
\( 960^3 + 744 = 884736744 \)
\( \exp{ \pi \sqrt{43}} = 884736743. 999777... \)
Heegner number d, (the ring of algebraic integers of \( \mathbb {Q} \left[{\sqrt {-d}}\right] \) has unique factorization)
Jacobsthal number: a(n) = a(n-1) + 2*a(n-2), with a(0) = 0, a(1) = 1; also a(n) = nearest integer to 2^n/3. n = 7
Factors: 1, 43
Representations, Binary to Hexadecimal:
101011_2
1121_3
223_4
133_5
111_6
61_7
53_8
47_9
3a_11
37_12
34_13
31_14
2d_15
2b_16
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