Recent content by nocat2

To clarify, I am not looking to produce a large number of primes. I am looking to produce a small number of very large primes. In particular, I see this as a viable method to find a new largest prime. It's for sport, really.

I'm surprised nearly all the primes found were "very close to p(x)". Certainly, the closer the output is to p(x) the more likely it is to be prime - I'm just surprised they are very close.

Thanks for running that. No surprise the success rate decreases with increasing x. It is encouraging that the rate of decrease slows as fast as shown. It appears this method is at least 10 times as successful for 164 digit primes as would be expected from random guesses. I suggest it would...

In the search for large primes and semi-primes one should test numbers of the form N = p(x) - 2y^n Where p(x) is 3*5*7*11*...*x and x is some last prime in consecutive list. y>x and y is prime n is largest possible that yields positive N Smaller n works with reduced probability of prime.

No, not at all related.

The data I gave is off slightly (I was using a printout of primes without having my reading glasses) but the numbers are close enough. Form is T=a-x^n Works nicely for n>=2 so long as T (test) remains positive. Is this form of interest?

Before I disclose that, I would like to know if these results are of interest. Input 27 prime numbers from 23 through 149 and the output gives 17 of 27 as six-digit primes. Remaining 10 are almost entirely six-digit semi-prime.

Not of the form 4x^2+bx+c

My quadratic(s) are not of that form and I suspect the one I have tested is 27 times more likely to generate a six-digit prime than by chance.

I'm familiar with that quadratic, and no, mine is different. Also note, the quadratic I have is exceptionally prime rich - when inputs are primes. And I suspect there will prove to be hundreds of thousands of these quadratic types that will be similarly prime rich. Oh, and quadratics are only...

How about this: I have a quadratic function that gives >50% prime and >40% semiprime results for any prime number input less than 350. The results are majority six-digit primes.

And of course with larger number digits generated, the greater the savings on required first primes. From what I can see, the savings (time, processing) would be substantial.

Well, I guess mine would have the advantage that it only requires the first 7 primes for a six-digit generated prime, so it is possibly twice as fast.

My algorithm is not so much a test for primality as it is a generator of primes (and semi-primes with at least one factor significantly greater than input).

Yes, thanks. I am aware of the many false claims made in this particular area. Note that I referred to my method as an algorithm. It certainly is conducive to programing but is not an algebraic solution. Also, I propose that outputs are rich in primes, not that they are always primes...