((A)-(A^2)+1)*(13))*(A)*((A)+(A^2)+1)*(13))=B, fits a model
- 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
-> 41,280,160,361,370, the center
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:
Squarefreely 0(7), or else 2(7) not congruent to 5(49), or 3(7)
not congruent to 10(49)
2, 5, or 6(13)
Squarefreely 0 or else 14(29), etc.
Would anyone want to search for primes using this method?
- Hi Gerald,
I m not a mathguy, but i would like to show you a different approach,
which brings up rather similar findings regarding to multiples of 210,
surrounded by +/- six prime-candidates.
Paint on paper a sieve
(http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes ) with the wide of
a primorial ( http://en.wikipedia.org/wiki/Primorial ). In your case
2x3x5x7. Now wipe out only all mulitples of 2, 3 and 5. It will result
into a sieve with straight lines down. Straight lines down mean, that
beside that lines you get allways potential primes, which are
definetly not multiples of 2,3,5. Also it creates a pattern, which you
can express in multiples of [210 +/-(1,7,11,13,17,19,23,29)] Compare
it with your findings now.
I dont know how you came up with your formula, but I think the
primorial-way is an alternative possibility to get the same in result?
It should also be possible to have similar findings in other primorial
ranges. So for example you may find (but it shouldnt be so easy)
Primes-patterns within Multiples of (2310 +/- (all whats left if you
wipe out all multiples of 2,3,5,7 within range of 2310)). The problem
is, as higher as you step on, you will get within that pattern mostly
only potential primes, which turn out as composits of primes higher
than for example 2,3,5,7 in the 2310-example later.
I wounder for some time now, why this connection isnt used regulary in
computer-searches for great primes, but i guess it has some cpu-reason...
(Sorry if I got something wrong, someone correct me then, i just like
the pattern-part of numbers, in general math I got actually pretty bad
marks in school and with computer science you can hunt me =p)