## 19084((A)-(A^2)+1)*(13))*(A)*((A)+(A^2)+1)*(13))=B, fits a model

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• Sep 13, 2007
To all interested:

Sometimes there's a multiple of 210 that's symmetrically surrounded
by twelve primes, six on both sides, by distances of 1, 11, 13, 17,
19, and 23. It's referred to as a prime galaxy center. An example
appears below:

41,280,160,361,347

41,280,160,361,351

41,280,160,361,353

41,280,160,361,357

41,280,160,361,359

41,280,160,361,369
-> 41,280,160,361,370, the center
41,280,160,361,371

41,280,160,361,381

41,280,160,361,383

41,280,160,361,387

41,280,160,361,389

41,280,160,361,393

There may be a way to obtain (not this very one but) sequences like
this by this formula:

First obtain an A that fits certain congruence class criteria (will
be shown later). Then subtract the same quantity from it as you add
to it, multiplying the three factors together:

((A)-((A^2)+1)*(13))*(A)*((A)+((A^2)+1)*(13))=B, B fitting some
proper subset for the general prime galaxy model.

If B is squarefree, then A is congruent to:

2(4)

3(9)

Squarefreely 0(5)

Squarefreely 0(7), or else 2(7) not congruent to 5(49), or 3(7)
not congruent to 10(49)

3(11)

2, 5, or 6(13)

7(17)

9(19)

5(23)

Squarefreely 0 or else 14(29), etc.

Would anyone want to search for primes using this method?

Owen Jarand
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