67 is a Prime Number
67 = 1 + 23 + 4 + 5 × 6 + 7 + 8 + 9
67 = 9 + 8 + 7 + 6 × 5 + 4 + 32 × 1
67 = 0^4 − 1^8 − 2^6 − 3^9 + 4^7 + 5^5 + 6^3 + 7^0 + 8^1 + 9^2
67 = 3^2 + 3^2 + 7^2
67 = 11 × (1 + 1) × (1 + 1 + 1) + 1
= 2(2+2+2) + 2 + 2/2
= (3 + 3/3)3 + 3
= 4 + (44 − 4)/4
= 55 + (55 + 5)/5
= 66 + 6/6
= 77 − (77 − 7)/7
= 8 × 8 − 8 + 88/8
= 9 × 9 − (99 + 9 + 9 + 9)/9
Sexy Prime (Primes p such that p + 6 is also prime)
Prime of the form 4*k^2 + 4*k + 59, k=2
675 = 135 + 185 + 235 + 315 + 365 + 665
675 = 75 + 205 + 295 + 315 + 345 + 665 =
\( \exp{ \pi \sqrt{67}} \approx 5280^3 + 744 \)
Weak veryprime
67 is an irregular prime, since it divides the numerator of the Bernoulli number B58.
e^(π sqrt(67))≈147197952743.9999987 is a near-integer
The ring of integers of the field Q(sqrt(-67))
Factors: 1, 67
Sixty-seven
Representations, Binary to Hexadecimal:
1000011_2
2111_3
1003_4
232_5
151_6
124_7
103_8
74_9
61_11
57_12
52_13
4b_14
47_15
43_16
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