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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]

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

Some integers
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

  1. 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.