# Algorithm for finding twin primes

I propose algorithm for finding twin primes:

Positive integers which do not appear in all four arrays $$A1(i,j)=6i^2+(6i−1)(j−1)$$, $$A2(i,j)=6i^2+(6i+1)(j−1)$$, $$A3(i,j)=6i^2−2i+(6i−1)(j−1)$$ and $$A4(i,j)=6i^2+2i+(6i+1)(j−1)$$

                    |  6   11    16     21   ...|
A1(i,j) =   | 24   35     46    57   ...|
| 54   71     88   105   ...|
| 96  119    142   165   ...|
|...  ...  ...   ...     ...|

|  6    13   20    27   ...|
A2(i,j) =   | 24    37   50    63   ...|
| 54    73   92   111   ...|
| 96   121  146   171   ...|
|...   ...  ...   ...   ...|

| 4       9     14       19.. |
|20      31     42       53...|
|48      65     82       99...|
A3(i,j)= |88     111     134     157...|
|...   ...      ...     ...   |

| 8      15      22     29 ..|
|28     41       54     67...|
A4(i,j)= |60     79       98     117..|
|104   129      154    179...|
|...    ...     ...     ...  |


are index $$k$$ of twin primes in the sequences $$S1(k)=6k-1$$ and $$S2(k)=6k+1$$.

So twin primes are:

$$5, 7(k=1)$$ .. $$11, 13(k=2)$$ ..$$17, 19(k=3)$$ .. $$29, 31(k=5)$$....

Is proposed algorithm for finding twin primes well-known?

• The algorithm you propose is essentially known in various forms. See this question: math.stackexchange.com/questions/2876402/… and answers to it Commented Feb 24, 2020 at 15:57
• But the formulae for composite numbers have the different form $6i^2+(6i-1)(j-1)$... etc .. and proposed algorithm is based on "matrix sieve" - see academia.edu/13890086/… Commented Feb 24, 2020 at 16:44
• Commented Feb 24, 2020 at 16:56
• Commented Feb 24, 2020 at 17:27