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The pairs $6h-1$ and $6h+1$ are not twin primes, that is at least one of them is factorizable/decomposable, where $h$ can be found from any of the following equations:

$$ \begin{align} h = 6t_1t_2 +7t_1+5t_2+6\;,\\ h = 6t_1t_2 +5t_1+5t_2+4\;,\\ h = 6t_1t_2 +7t_1+7t_2+8\;.\\ \end{align} $$

Here $h$ is the third integer coordinate of the points of the paraboloids obtained by integer values of $t_1$ and $t_2$, where $t_1$ and $t_2$ belongs to $N\cup\{0\}$.

Now, can you explain how to support the statement cited above, if I am correct. Or else, let me know where I am wrong.

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    What is N?$\text{}$2012-10-31
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    @ N is set of Natural numbers. N = {1, 2, 3, 4, ...}2012-10-31
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    @N union 0 is = {1,2,3,...} U {0}2012-10-31

1 Answers 1