hypothese on some prime
 

I have an hypothese where for all number on 6n-1 and on 11,17,23,29+30a, if its not factoring by any: (6a-1) (6a+1) on where 6a-1 is on 11,17,23,29+30c and 6a+1on 7,13,19,31+30bthen its prime. If it appears to be true would it be good to confirm a prime on 6n-1 not on 5+30n, 25+30n

[QUOTE=Capncrap;459022]I have an hypothese where for all number on 6n-1 and on 11,17,23,29+30a, if its not factoring by any: (6a-1) (6a+1) on where 6a-1 is on 11,17,23,29+30c and 6a+1on 7,13,19,31+30bthen its prime. If it appears to be true would it be good to confirm a prime on 6n-1 not on 5+30n, 25+30n[/QUOTE]

all primes greater than 3 are of one of the forms 6a+1 or 6a-1 this can be proved in remainder math. the reason 5+30n and 25+30n aren't prime is because they factor as 5*(1+6n) and 5*(5+6n) the primes themselves don't include every member of 6a+1 or 6a-1 though some are composites which factor into primes of those forms. like 25 is (6n+5)^2 for n=0. as to different numbers +30n being prime this is also talked about in remainder math if both parts of the sum share a factor greater than 1 we can prove that it's not prime because the parts share a factor ( and so the sum of them must have that factor). in general the primes are only on the remainders that are coprime ( don't share a factor other than 1) on division by any numbers however once again not all numbers of these forms are necessarily prime.

[QUOTE=Capncrap;459022]if its not factoring by any: (6a-1)[COLOR=Red]?[/COLOR](6a+1)[/QUOTE]
If the red question mark (which I added) is an ”or”, than your "hypothese" is true, and obvious. All primes, are by definition, "not factoring by" other primes (which are all either 6a-1, either 6a+1).

If the red question mark is supposed to be a product, than your "hypothese" is false. There are composite numbers that have factors which are not a product of other 2 factors. They are called prime factors. Now, ok, if you multiply (-1)(mod 6) and (1)(mod 6), you get either 5, 11, 17, 23, 29, (mod 30), and of course that any composite in these modular classes must be a multiple of that product.

To reformulate: "I have a hypothese, any number which is not divisible by other number except 1 and itself, is prime". As you said, "cap and crap"...

Well even if my education stopped right before complex number, thanks for call me a crap, lol, that is true I didnt define any limit where 6n-1 and 6a-1 share same equations when 6n-1 * 6a-1 >= 6b+1

6n-1 >=7( 6a-1 )and both on 11,17,23,29+30c
6n-1>= 11(6b+1) where 6b+1 is on 7,13,19,31+ 30d

My question is how long would it be for a computer to calculate all (6a-1)(6b+1) until a certain 6n-1 on 11,17,23,29,30+30c, where all my freaking variables are on naturals positives so from there soustration of the sums of all possible (6a-1)(6b+1), between 6(n+1)-1 and 6n+1 on the same freaking equations should be 0 for a prime and 1 on non prime.

[QUOTE=Capncrap;459039]Well even if my education stopped right before complex number, thanks for call me a crap, lol, that is true I didnt define any limit where 6n-1 and 6a-1 share same equations when 6n-1 * 6a-1 >= 6b+1

6n-1 >=7( 6a-1 )and both on 11,17,23,29+30c
6n-1>= 11(6b+1) where 6b+1 is on 7,13,19,31+ 30d

My question is how long would it be for a computer to calculate all (6a-1)(6b+1) until a certain 6n-1 on 11,17,23,29,30+30c, where all my freaking variables are on naturals positives so from there soustration of the sums of all possible (6a-1)(6b+1), between 6(n+1)-1 and 6n+1 on the same freaking equations should be 0 for a prime and 1 on non prime.[/QUOTE]

well 6n-1 and 6n+1 are arithmetic progressions so you're asking about sieving out the composites we can get:

a multiplication of two potentially different 6n-1:

(6k-1)(6j-1)=36kj-6k-6j+1 = 6(6kj-k-j)+1

a multiplication of two potentially different 6n+1:

(6k+1)(6j+1)= 36kj+6k+6j+1 = 6(6kj+k+j)+1

or a multiplication of a 6n+1 by a 6n-1:

(6k+1)(6j-1)=36kj-6k+6j-1 = 6(6kj-k+j)-1

assuming one of these values in the multiplication isn't 1 these are all composite. you can also use the fact that if prime r divides even one r will divide every r th one etc.

So its possible that a number on 11, 17,23,29+ 30n that is not prime, could be factoring by other number than (11,17,23,29+30a)(7,13,19,31+30b), can iget an example? Where there are somes logicals limits. In my opinion there is no formula for prime but an absence of solution for all possible primes on ,7,11,13, 19,23,29, 31+30n, also i think prime is a relation to multiple of 6 but whatever, ill leave theses researchs to high end brain, cause I cant sleep since I started to work on it.

[QUOTE=Capncrap;459057]So its possible that a number on 11, 17,23,29+ 30n that is not prime, could be factoring by other number than (11,17,23,29+30a)(7,13,19,31+30b), can iget an example?[/QUOTE]

Let me see if I understand. Are you asking
[INDENT]Is there an example of a composite number which is 11, 17, 23, or 29 mod 30 which is not of the form ab where a is 11, 17, 23, or 29 mod 30 and b is 1, 7, 13, or 19 mod 30?[/INDENT]

For example, 161, is on 11+30n , and 6a-1, his factors are 7 and 23 then, it,s like (6b+1)*(6c-1) = 6n-1 , is there any form of (6b+1)(6c+1) or (6b-1)(6c-1) = 6n-1, excluding 5,25+30n demonstration on a forum but they say it,s weak because I have no knowledge for demonstration. But if my hypothese is true think i would be easy to determine if a number on 6a-1 is prime.

If you know the number of false prime on 6n-1 under n/7, then all possibilities:

11 * | 7, 13, 19, 31, 37, until 11*a<= n/7
17
23
29

...
Until Closest number to n/7

then you want to test the closest number over last one, but the limits of n/7 will change and it can produce new factors , but since those 2 numbers are close, they share a lot of same factors under n/7, in my opinion if theyre is no new solution, than your number should beprime

Also on a cycle of 30 they re 4 possibilities for 6n-1, so its easy to determine how manysolutions you can get on a number

[QUOTE=Capncrap;459069]For example, 161, is on 11+30n , and 6a-1, his factors are 7 and 23 then, it,s like (6b+1)*(6c-1) = 6n-1 , is there any form of (6b+1)(6c+1) or (6b-1)(6c-1) = 6n-1, excluding 5,25+30n demonstration on a forum but they say it,s weak because I have no knowledge for demonstration. But if my hypothese is true think i would be easy to determine if a number on 6a-1 is prime.

If you know the number of false prime on 6n-1 under n/7, then all possibilities:

11 * | 7, 13, 19, 31, 37, until 11*a<= n/7
17
23
29

...
Until Closest number to n/7

then you want to test the closest number over last one, but the limits of n/7 will change and it can produce new factors , but since those 2 numbers are close, they share a lot of same factors under n/7, in my opinion if theyre is no new solution, than your number should beprime

Also on a cycle of 30 they re 4 possibilities for 6n-1, so its easy to determine how manysolutions you can get on a number[/QUOTE]

you realize that multiplying any two from the same side of a multiple of 6 either the negative side or the positive side doesn't give you a negative side number right ...

I predicted 83 primes on (0-1000) on 11,17,23,29+30p

1000/11 ->90,90 -> 90
1000/7 -> 142.85 -> 142

So i know 90 is max on 7,13,19,31+30q
And 142 max on 11,17,23,29+30r

So: possible answer

1000/30 :33.333 but between 990 and 1000 there is nothing cause 11+30(33)=1001
Then 33 group of 4 possibilities : 132

So we can calculate non prime number

11 *| 7, 13,19,31,37,43,49,61,67,73,79 -> 11 possibilities
17*| 7,13,19,31,37,43,49 -> 7 possibilities
23*| 7,13,19,31,37,43 -> 6possibilities
29*| 7, 13,19,31 -> 4 possibilities
41* | 7,13,19 -> 3
47*| 7,13,19 -> 3
53*| 7,13-> 2
59*|7,13 -> 2
71*| 7,13 -> 2
77*| 7 ->1
83 *| 7->1
89. -> 1
101 ->1
107->1
113 ->1
119 -> 1
131-> 1
137->1
For a total of 49 possibilities
132-49 = there are 83 primes on 6n-1 between0-1000

Under my rule , 6p-1=( 6q-1)(6r+1)
6q-1= 6s-1 * 6t+1 you can keep going
6r+1 is -1 * -1 or +1*+1 ->> (-1*+1) * (-1*+1) but always remind 6r+1
So my logic is if there at least one 6q-1 or 6r+1 that divide 6p-1 then its non prime

[QUOTE=Capncrap;459143]I predicted 83 primes on (0-1000) on 11,17,23,29+30p[/QUOTE]

If you want to estimate the number of primes in residue classes {a1, ..., an} mod m in [x, y] where y - x is large compared to m, just count the number of a1, ..., an which are relatively prime to m, divide by phi(m), then multiply by (y - x)/log y. In your case this is 4/phi(30) * (1000 - 0)/(log(1000) - 1) or about 85. The error should be around the square root of the predicted quantity, so 76 to 94 would be a reasonable range to expect.

Could we predict a prime if we evalutate his limits over the last 6n-1. If his limits are the same then there is no new false prime between them

For example n1/7 = 60.2
n2/7= 60.9

n1/ 11= 30.8
n2/11= 30.9
So these numbers share the same false prime and no new false prime between closest 2 possible primes, it was an exemple but could this work

I don't understand what you're suggesting. Could you use this method to test whether 50851 is prime?

It has to be build from 11 to infinite I think but, im not sure cause it depends on previous data and it would push back until we know the nature of that number

Huh? Are you saying we won't know the [primality] nature of the number until we know the nature of the number? I mean, that's like saying you can only test your method for primality on numbers that are prime.

Can your method make predictions, or not? If you can only make predictions based on having a list of previous primes, we have faster methods that work like that (sieves).

He started by saying that every number which is 11, 17, 23, 29 (mod 30) [note that in this case the number is -1 (mod 6) trivial] is prime, if and only if it does not have a factor of the form ((-1)(mod 6))\(\cdot\)((1)(mod6)), which is obvious. The rest is blabbing around the tail.
One vote to be moved to Misc Math.

Youre right, I only wanted to share what Im getting from basic education, it cant says if a number is prime unless you create an infinite table with all values 8\30 where you calculate the multiplication of all possible factors {11,17,23,29+30a}, And {7,13,19,31+30a} I thought my hypothese could have helped cause it delete a lot of value 8 numbers on 30, but be sure I knew there was greater intelligence under theses walls.

[QUOTE=Capncrap;459212]Youre right, I only wanted to share what Im getting from basic education, it cant says if a number is prime unless you create an infinite table with all values 8\30 where you calculate the multiplication of all possible factors {11,17,23,29+30a}, And {7,13,19,31+30a} I thought my hypothese could have helped cause it delete a lot of value 8 numbers on 30, but be sure I knew there was greater intelligence under theses walls.[/QUOTE]

a modular multiplication table for mod 30 for those values:

[TEX]\begin{tabular}{ l | l | c | c | c | c | c | c | c | r | }
& 1 & 7 & 11 & 13 & 17 & 19 & 23 & 29 \\ \hline
1 & 1 & 7 & 11 & 13 & 17 & 19 & 23 & 29 \\ \hline

7 & 7 & 19 & 17 & 1 & 29 & 13 & 11 & 23 \\ \hline

11 & 11 & 17 & 1 & 23 & 7 & 29 & 13 & 19 \\ \hline

13 & 13 & 1 & 23 & 19 & 11 & 7 & 29 & 17 \\ \hline

17 & 17 & 29 & 7 & 11 & 19 & 23 & 1 & 13 \\ \hline

19 & 19 & 13 & 29 & 7 & 23 & 1 & 17 & 11 \\ \hline

23 & 23 & 11 & 13 & 29 & 1 & 17 & 19 & 7 \\ \hline

29 & 29 & 23 & 19 & 17 & 13 & 11 & 7 & 1 \\ \hline
\end{tabular}[/TEX]

[QUOTE=LaurV;459184]He started by saying that every number which is 11, 17, 23, 29 (mod 30) [note that in this case the number is -1 (mod 6) trivial] is prime, if and only if it does not have a factor of the form ((-1)(mod 6))\(\cdot\)((1)(mod6)), which is obvious.[/QUOTE]

I see, thank you. So it can't say anything about 50851 because it's 1 mod 6, but it says that I could test if 54149 is prime by testing all the numbers 1 mod 6 up to 54149/5 to see if they're factors. Or as an enhancement, I could test all the numbers 1 mod 6 (equally, 5 mod 6) up to sqrt(54149) and then all the numbers 5 mod 6 up to sqrt(54149). :smile: So it's just one step behind trial division with a mod 6 wheel, and two steps behind trial division with primes.