hypothese on some prime

[CRGreathouse]

Originally Posted by Capncrap

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

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.

[Capncrap]

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

[CRGreathouse]

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

[Capncrap]

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

[VBCurtis]

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).

[LaurV]

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.

[Capncrap]

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.

[science_man_88]

Originally Posted by Capncrap

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.

a modular multiplication table for mod 30 for those values:

[CRGreathouse]

Originally Posted by LaurV

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.

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). So it's just one step behind trial division with a mod 6 wheel, and two steps behind trial division with primes.