Shor's Algorithm - periodicity table 1

Table 1 shows periodicity of Shor's Algorithm for prime numbers combinations between 3 and 47 for type 1 or T1.

x 3 5 7 11 13 17 19 23 29 31 37 41 43
3 x 6 4 18 28
5 x 12 20 2 16 40 84
7 6 12 x 12 8 12 36 42
11 20 x 90 140 30 180 40
13 2 12 x 18 44 60 84
17 4 16 8 x 2 88 56 240 144 80 28
19 18 90 18 2 x 36 180 126
23 44 88 x 154 330 220 154
29 28 12 140 56 154 x 420 252 280
31 30 60 240 330 420 x 180 120
37 36 180 144 36 252 180 x 60 84
41 40 40 80 180 220 280 120 60 x 210
43 84 42 84 28 126 154 84 210 x
47 92 230 276 92 414 276 966
Table 1: Periodicity table from 1 to 43

Shor's Algorithm - table 2 - x values

Table 2 shows x values for prime numbers combinations between 3 and 47

x 3 5 7 11 13 17 19 23 29 31 37 41 43
3 x 9 10 12 12 13 13 14 14 15 15 15 16
5 9 x 12 13 14 14 15 15 16 16 17 17 17
7 10 12 x 14 15 15 16 16 17 17 18 18 18
11 12 13 14 x 16 17 17 17 18 18 19 19 19
13 12 14 15 16 x 17 17 18 19 19 19 20 20
17 13 14 15 17 17 x 18 19 19 20 20 20 21
19 13 15 16 17 17 18 x 19 20 20 20 21 21
23 14 15 16 17 18 19 19 x 20 20 21 21 21
29 14 16 17 18 19 19 20 20 x 21 22 22 22
31 15 16 17 18 19 20 20 20 21 x 22 22 22
37 15 17 18 19 19 20 20 21 22 22 x 23 23
41 15 17 18 19 20 20 21 21 22 22 23 x 23
43 16 17 18 19 20 21 21 21 22 22 23 23 x
47 16 17 18 20 20 21 21 22 22 23 23 23 23
53 16 18 19 20 20 21 21 22 23 23 23 24 24
Table 2: Periodicity table from 1 to 43

Shor's Algorithm - periodicity table 3

Table 3 shows the solution of Shor's Algorithm for prime numbers combinations between 47 and 103.
The right upper part shows the solution type T1, T3 or T4 for each combination.
The left bottom part shows the periodicity for each prime number combination.

x 47 53 59 61 67 71 73 79 83 89 97 101 103
47 x T3 T1 T1 T3 T3 T1 T3 T3 T1 T1 T1 T1
53 299 x T1 T1 T1 T1 T1 T1 T1 T1 T1 T1 T1
59 1334 754 x T3 T3 T1 T1 T3 T3 T1 T1 T1 T1
61 460 390 435 x T3 T1 T1 T1 T1 T1 T1 T1 T4
67 253 286 319 165 x T1 T1 T3 T3 T1 T1 T1 T4
71 115 130 406 420 462 x T1 T1 T3 T1 T1 T1 T1
73 828 468 2088 360 792 504 x T1 T1 T1 T1 T1 T1
79 897 156 1131 780 429 546 936 x T1 T1 T1 T1 T4
83 943 2132 1189 2460 1353 1435 164 1066 x T1 T1 T1 T3
89 2024 1144 2552 1320 88 3080 88 1144 3608 x T1 T1 T1
97 2028 1248 2784 80 176 560 16 208 656 352 x T1 T1
101 2300 2300 2900 100 1100 700 100 1300 4100 2200 800 x T1
103 2346 2652 986 170 374 1190 68 442 2091 4488 1632 5100 x

Table 3: Periodicity table from 47 to 43

In total there are 61 of T1, 14 of T3 and 3 of T4

Created: 6 January 2003
updated: 4 April 2003
Updated: 21 Oktober 2015

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