1 No. not factorable by 2 in (2)

There are 2 No.'s not factorable by 2 or 3 in (6)

There are 8 No.'s not factorable by 2 or 3 or 5 in (30)

There are 48 No.'s not factorable by 2 or 3 or 5 or 7 or in (210)

times 48 by (prime -1) to get the next number of no.'s. i.e. =480 no.'s in (2310) not factorable by 2,3,5,7, or 11.....and so on.]]>

6+/-1 5..

30+/- 1 7..

210 +/- 1 11..

2310 +/- 1 13..

equals primes......to a certain point above highest prime squared. e.g.>9,25,49,121 or 169 accordingly. And so on but the numbers get very big but you can do this up to infinity.

]]>http://en.wikipedia.org/wiki/Largest_known_prime_number

How is 17,425,170 a prime number? It is divisible by 2.

Thanks

It clearly says in plain English that this number is the number of digits of the largest known prime number. You're welcome?

]]>x = prime

y = anything other than 1 and x

z = composite

a = decimal

x/1=x. x/x=1. x/y=a.

z/1=z. z/z=1. z/y=y.

For something else on prime numbers... go to my Sieve of Eratosthenes post.]]>

Welcome to the forum!

]]>Welcome to the forum!

]]>For prime numbers (r), under 5 squared; r = 3p +/- 2 or 4

For prime numbers (i), under 7 squared; i = 5r +/- 6 or 12 or 18 or 24

For prime numbers (m), under 11 squared; m = 7i +/- 30 or 60 or 90 or 120 or 150 or 180

For prime numbers (e), under 13 squared; e = 11m +/- 210 or 420 or 630 or 840 or 1050 or 1260 or 1470 or 1680 or 1890 or 2100

(A no. divisible by a, but not divisible by a group b +/- A no. divisible by group b, but not a = A no. not divisible by a or b.)

* Some rules give 1 but this is not prime.

]]>I am looking for one. I have one written for Mathematica but not for anything else just yet.

The Miller - Rabin does not need to factor the number. It is quite fast, but it is not deterministic. It can only provide a probabilty that the number is composite. Of course this probabilty can be made very, very small.

]]>I haven't try AKS method yet, if you could provide me the link of any program using that method let me know. I know, ECM is not for proving and disproving but the guy had incorporated Rabin-Miller probabilistic test in the program and it would tell you whether the number is prime or not at the end of factorization. Anyway, it would be a great help if you could provide me a link where to download or use AKS method. For your information I haven't got into programming for quite long time and to write a program for checking primality on my own would take some times.

By the way, thanks for your suggestion and idea it is a great help.

]]>Depends on what you mean by better. The ECM is for factoring a number not for proving or disproving primality. Factoring is much harder problem than proving primality.

There are two types of tests for primality that I know of. The AKS developed by 3 Indian fellows and Rabin Miller which is a probabilistic test.

]]>I am running quad core i5 with 8gb memory and it took me around a day to check the primality of that 2241 digits prime. I am using ECM program written by an Argentinian's programmer. You can get his program at alpertron dot com dot ar. His program only could test up to 20,000 digits. I think if someone could write a primality checker for larger prime using the formulation I got, it would be kool. I am working to get first 1 million digits prime using the formulation but I think it is going to take for ages. Got a friend who tried to write the program but he quit. Can you suggest me the better way to check the primality accurately and fast? From the equation, theoretically we could get bigger prime than the Mersenne because it allows bigger numbers in the equation.

]]>You are welcome!

My limitation is that I need bigger computing power to check for the primality test.

What method are you using? If you are using ECM there are better ways.

]]>You are welcome and thanks for your latex link.

]]>Thanks for explaining your idea.

]]>