37 is a Prime Number, Prime(12)
37 = 1 + 23 − 4 − 5 − 67 + 89
37 = 98 − 76 − 5 − 4 + 3 + 21
37 = 0^4 + 1^8 − 2^6 − 3^9 + 4^7 + 5^5 + 6^3 + 7^2 + 8^1 + 9^0
37 = 1^2 + 6^2
37^2 = 12^2 + 35^2
37 = 111/(1 + 1 + 1)
= (2 + 2 + 2)2 + 2/2
= 3 + 33 + 3/3
= 4 + 4 × (4 + 4) + 4/4
= 5 + ((5 + 5)/5)5
= 6 × 6 + 6/6
= 777/(7 + 7 + 7)
= 888/(8 + 8 + 8)
= 999/(9 + 9 + 9)
\( 37^2 = 12^2 + 35^2 \)
Sexy Prime (Primes p such that p + 6 is also prime)
37 is an irregular prime, since it divides the numerator of the Bernoulli number B32 = -7709321041217/510.
Part of the Cunningham chain of the second kind 19, 37, 73
a(n) = 3^n + 3*n + 1, n = 3
a(n) = 2^n + n, n = 5
37 = 17+17+3, 17+13+7, 17+17 13+13+11 Goldbach partitions
Number k such that (7*10^k + 71)/3 is prime.
Numbers k such that 2^k + 9 is prime
Centered 12-gonal number, or centered dodecagonal number: number of the form 6*k*(k-1) + 1.
\( 37^4 \approx 21^4 + 36^4 \) Fermat approximate solutions
e^(π sqrt(37))≈199148647.999978 is a near-integer.
The ring of integers of the associated field Q(sqrt(-148)) has class number 2.
Factors: 1, 37
Thirty-seven
Representations, Binary to Hexadecimal:
100101_2
1101_3
211_4
122_5
101_6
52_7
45_8
41_9
34_11
31_12
2b_13
29_14
27_15
25_16
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