59 is a Prime Number, Prime(17)
Part of the Cunningham chain 29, 59
59 = 1 × 2 × 3 × 4 + 5 + 6 + 7 + 8 + 9
59 = 9 + 8 + 7 + 6 + 5 + 4 × 3 × 2 × 1
59 = 0^5 + 1^9 − 2^7 − 3^8 + 4^6 + 5^2 + 6^3 + 7^4 + 8^1 + 9^0
Safe prime p: (p-1)/2 is also prime
Prime of the form 4*k^2 + 4*k + 59, k=1
Number of fractions in Farey series of order 13: 0/1, 1/13, 1/12, 1/11, 1/10, 1/9, 1/8, 1/7, 2/13, 1/6, 2/11, 1/5, 2/9, 3/13, 1/4, 3/11, 2/7, 3/10, 4/13, 1/3, 4/11, 3/8, 5/13, 2/5, 5/12, 3/7, 4/9, 5/11, 6/13, 1/2, 7/13, 6/11, 5/9, 4/7, 7/12, 3/5, 8/13, 5/8, 7/11, 2/3, 9/13, 7/10, 5/7, 8/11, 3/4, 10/13, 7/9, 4/5, 9/11, 5/6, 11/13, 6/7, 7/8, 8/9, 9/10, 10/11, 11/12, 12/13, 1/1
59 = (11(1+1) − 1)/(1 + 1) − 1
= 2 × (22 + 2) + 22/2
= 33 + 33 − 3/3
= (44 − 4)/4 − 4
= 55 + 5 − 5/5
= 66 + 6 − 6/6
= 77 − 7 − 77/7
= 8 × 8 − 8 − 8 + 88/8
= 9 + (9 × 99 + 9)/(9 + 9
Smallest number whose sum of digits is 14.
59 is an irregular prime, since it divides the numerator of the Bernoulli number B44
e^(π sqrt(59))≈30197683486.9932
The ring of integers of the field Q(sqrt(-59)) has class number 3
Factors: 1, 59
Fifty-nine
Representations, Binary to Hexadecimal:
111011_2
2012_3
323_4
214_5
135_6
113_7
73_8
65_9
54_11
4b_12
47_13
43_14
3e_15
3b_16
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