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73
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73 is the 21st prime number, and in base 10 it happens that the 12th prime number is 37.^{[1]}
Contents
- 1 Membership in core sequences
- 2 Sequences pertaining to 73
- 3 Partitions of 73
- 4 Roots and powers of 73
- 5 Logarithms and 73rd powers
- 6 Values for number theoretic functions with 73 as an argument
- 7 Factorization of some small integers in a quadratic integer ring adjoining the square roots of −73, 73
- 8 Factorization of 73 in some quadratic integer rings
- 9 Representation of 73 in various bases
- 10 See also
- 11 References
Membership in core sequences
Odd numbers | ..., 67, 69, 71, 73, 75, 77, 79, ... | A005843 |
Prime numbers | ..., 61, 67, 71, 73, 79, 83, 89, ... | A000040 |
Lucky numbers | ..., 63, 67, 69, 73, 75, 79, 87, ... | A000959 |
Squarefree numbers | ..., 69, 70, 71, 73, 74, 77, 78, ... | A005117 |
Numbers that are the sum of two squares | ..., 65, 68, 72, 73, 74, 80, 81, ... | A001481 |
Loeschian numbers | ..., 63, 64, 67, 73, 75, 76, 79, ... | A003136 |
Sequences pertaining to 73
Multiples of 73 | 73, 146, 219, 292, 365, 438, 511, 584, 657, 730, 803, 876, ... | |
sequence beginning at 73 | 73, 220, 110, 55, 166, 84, 42, 21, 64, 32, 16, 8, 4, 2, 1, ... | |
sequence beginning at 11 | ..., 146, 73, 366, 183, 916, 458, 229, 1146, 573, 2866, 1433, ... |
Partitions of 73
There are 6185689 partitions of 77. Of these, the of the [FINISH WRITING]
Roots and powers of 73
In the table below, irrational numbers are given truncated to eight decimal places.
TABLE GOES HERE
Logarithms and 73rd powers
REMARKS
TABLE
Values for number theoretic functions with 73 as an argument
TABLE GOES HERE
Factorization of some small integers in a quadratic integer ring adjoining the square roots of −73, 73
The commutative quadratic integer ring with unity , with units of the form (), is not only a unique factorization domain, it is also a norm-Euclidean domain, and in fact no quadratic integer ring with higher discriminant is norm-Euclidean (but there are higher with unique factorization).
2 | |
3 | |
4 | |
5 | Prime |
6 | |
7 | Prime |
8 | |
9 | |
10 | |
11 | Prime |
12 | |
13 | Prime |
14 | |
15 | |
16 | |
17 | Prime |
18 | |
19 | |
20 |
Note that does not constitute a distinct factorization of 6 since .
is not a unique factorization domain. But the window of 1 through 20 does not provide as interesting a window for the of the [FINISH WRITING]
Factorization of 73 in some quadratic integer rings
PLACEHOLDER
TABLE GOES HERE
Representation of 73 in various bases
Base | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
Representation | 1001001 | 2201 | 1021 | 243 | 201 | 133 | 111 | 81 | 73 | 67 | 61 | 58 | 53 | 4D | 49 | 45 | 41 | 3G | 3D |
See also
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |
20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 |
30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 |
40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 |
1729 |
References
- ↑ Sheldon Cooper (Jim Parsons) points these tidbits out in the 73rd episode of The Big Bang Theory, "The Alien Parasite Hypothesis", written by Chuck Lorre, Steven Molaro & Steve Holland. The episode first aired on December 9, 2010.