The following table shows if Shor's Algorithm works for prime numbers combinations 3 and 5 (N=15):
a  6  7  8  9  10  11  12  13 
q  64  128  256  512  1024  2048  4096  8192 
type  2  1  1  2  2  1  2  1 
period  1  4  4  2  1  2  4  4 
y  6  4  4  9  10  11  12  4 
Box 1  Shor's algorithm

The following table shows if Shor's Algorithm works for prime numbers combinations 5 and 11:
a  9  10  11  12  13  14  15  16  17  18  19  20 
q  512  1024  2048  4096  8192  16384  32768  65536  131072  262144  524288  1048576 
type  1  2  2  1  1  1  2  3  1  1  4  2 
period  10  2  1  4  20  10  5  5  20  20  10  5 
What the above table shows that there are only T1 type of solutions (With stop sign and even periodicity) for a = 9,12,13, 16 and 17.
To find all the solutions use the "Findprime 2" application of the Excel program findprim.xls "Blad2"
pm1  pm2  n  a  q  type  period  y  p  q 
3  5  15  11  2048  T1  2  11  3  5 
3  5  15  19  524288  T1  2  4  5  3 
3  5  15  26  67108864  T1  2  11  3  5 
3  13  39  14  16384  T1  2  14  3  13 
5  11  55  21  2097152  T1  2  21  11  5 
5  13  65  14  16384  T1  2  14  5  13 
5  17  85  16  65536  T1  2  16  17  5 
5  19  95  39  5,49E+11  T1  2  39  5  19 
7  11  77  34  17179869184  T1  2  34  7  11 
7  13  91  27  134217728  T1  2  27  7  13 
7  17  119  50  1,1259E+15  T1  2  50  17  7 
11  13  143  12  4096  T1  2  12  13  11 
11  17  187  21  2097152  T1  4  67  17  11 
Box 3  Prescription

See Also: Shor's Algorithm Reflection 5  RSA768.
General performance increases linear with the length of the prime numbers involved. That means when the prime numbers are a factor 10 larger the performance also increases with a factor 10.
Using the Maxima package in order to factorize RSA768 execution time is than roughly 10^100 seconds. This is extremely large.
This raises three issues:
Back to my home page Index
Back to Nature comments Nature Index