0

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?

Boris Sklyar
  • 107
  • The algorithm you propose is essentially known in various forms. See this question: https://math.stackexchange.com/questions/2876402/a-twin-prime-theorem-and-a-reformulation-of-the-twin-prime-conjecture and answers to it – Keith Backman Feb 24 '20 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 https://www.academia.edu/13890086/Matrix_sieve_the_easiest_way_to_find_prime_numbers – Boris Sklyar Feb 24 '20 at 16:44
  • C++ code - see https://www.academia.edu/37724498/FINDING_TWIN_PRIMES_IN_THE_RANGE_N1_N2_ – Boris Sklyar Feb 24 '20 at 16:56
  • Also see http://www.planet-source-code.com/vb/scripts/BrowseCategoryOrSearchResults.asp?lngWId=3&blnAuthorSearch=TRUE&lngAuthorId=21687209&strAuthorName=Boris%20Sklyar&txtMaxNumberOfEntriesPerPage=25 – Boris Sklyar Feb 24 '20 at 17:27

0 Answers0