The two MLSG's shown represent the polynomials 1 + x⁴   and 1 + x² + x³ + x⁴ + x⁸, respectively.

For each n shown there is a MLSG based on a shift register with various outputs XOR-d together. For any initial state ( except all 0's) the MLSG produces a sequence of 0's and 1's having length 2ⁿ-1 before it repeats.

The polynomial shown is the simplest (fewest XOR's required) possible.

n	polynomial
1	1 + x
2	1 + x + x2
3	1 + x + x3
4	1 + x + x4
5	1 + x2 + x5
6	1 + x + x6
7	1 + x + x7
8	1 + x2 + x3 + x4 + x8
9	1 + x4 + x9
10	1 + x3 + x10
11	1 + x2 + x11
12	1 + x + x4 + x6 + x12
16	1 + x2 + x3 + x5 + x16
20	1 + x3 + x20
21	1 + x2 + x21
...	...
29	1 + x2 + x29
30	1 + x + x4 + x6 + x30
31	1 + x3 + x31

and some really long ones:
 

41	1 + x3 + x41
47	1 + x5 + x47
60	1 + x + x60
63	1 + x + x63
127	1 + x + x127

To find out more, see: Arthur Gill:
LINEAR SEQUENTIAL CIRCUITS, Analysis, Synthesis, and Applications,
McGraw Hill Book Co. New York, 1966