All twin primes after (29,31) are built as 30*k + (11,13) or +(17,19) or +(29,31)

Attached is a table for k from 1 to 20 showing their construction.

The assertion is that for every k which is prime, there is at least one

of the 3 additions which produces a twin prime.

(30)k +(11,13) -------+(17,19) ------+(29,31)

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1 -------(41,31) --------(47,49x)------- (59,61)

2p -----(71,73) --------(77x,79) -------(89,91x)

3p ----(101,103) -----(107,109) -----(119x,121x)

4 ------(131,133x) ----(137,139) -----(149,151)

5p ----(161x,163) ----(167,169x) ----(179,181)

6 ------(191,193) ------(197,199) -----(209x,211)

7p ----(221x,223) -----(227,229) ----(239,241)

8 ------(251,253x) -----(257,259x) ---(269,271)

9 ------(281,283) ------(287x,289x) --(299x,301x)

10 ----(311,313) ------(317,319x) ----(329x,331)

11p --(341x,343x) ---(347,349) -----(359,361x)

12 ----(371x,373) -----(377x,379) ---(389,391x)

13p --(401,403x) -----(407x,409) ---(419,421)

14 ----(431,433) -------(437x,439) ---(449,451x)

15 ----(461,463) -------(467,469x) ---(479,481x)

16 ----(491,493x) ------(497x,499) --(509,511x)

17p --(521,523) -------(527x,529x) -(539x,541)

18 ----(551x,553x) ----(557,559x) ---(569,571)

19 p -(581x,583x) -----(587,589x) --(599,601)

20 ----(611x,613) ------(617,619) ----(627x,631)

Milton L. Brown

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