57 is a Grothendieck prime
3nd (n=2) Hexagonal prism number \((n+1)(3n^{2}+3n+1),\)
57 = 1 + 2 × 3 + 4 × 5 + 6 + 7 + 8 + 9
57 = 9 + 8 + 7 + 6 + 5 × 4 + 3 × 2 + 1
57 = 0^5 − 1^9 − 2^7 − 3^8 + 4^6 + 5^2 + 6^3 + 7^4 + 8^1 + 9^0
57 , smallest number with 10 representations as a sum of 3 distinct primes: 57 = 3 + 7 + 47 = 3 + 11 + 43 = 3 + 13 + 41 = 3 + 17 + 37 = 3 + 23 + 31 = 5 + 11 + 41 = 5 + 23 + 29 = 7 + 13 + 37 = 7 + 19 + 31 = 11 + 17 + 29
57 = (111 + 1)/(1 + 1) + 1
= 2 × 22 + 2 + 22/2
= 33 + 33 + 3
= 4 + (44 − 44)/4
= 55 + (5 + 5)/5
= 66 + (6 + 6 − 66)/6
= 7 × 7 + 7 + 7/7
= 8 × 8 − 8 + 8/8
= (999 + 9)/(9 + 9) + 9/9
Number k such that k^2 + 2 is prime (3251)
Numbers k such that 2^k + 9 is prime
Number of edges in an equilateral triangle when n internal equilateral triangles are drawn between the 3n points that divide each side into n+1 equal parts. (n=3)
Maximal number of regions obtained by joining 7 points around a circle by straight lines
Number of distinct products i*j*k for 1 <= i <= j < k <= n, n = 8
Semiprime (Product of 2 Primes)
Factors: 1, 57
Fifty-seven
Representations, Binary to Hexadecimal:
111001_2
2010_3
321_4
212_5
133_6
111_7
71_8
63_9
52_11
49_12
45_13
41_14
3c_15
39_16
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