The fastest way to a top-5000 prime?

[Washuu]

I have tested k=5865 from N=200K to N=300K, on a few machines.

It took over one week with LLR.exe, I sieved to 77billions by newpgen.exe earlier.

Only one prime found, 5865*2^261351-1. I expected about 3-6... maybe just this number wasn't so lucky.

[Kosmaj]

BTW, I tested k=25935 from n=183500 to n=220000 and found one prime for n=219995 (already included in the table above). I don't plan to test this k any further.

I also tested k=67773 from n=183500 to n=236000 and found no primes. I have sieved to n=250000 and will stop there.

[Flatlander]

Originally Posted by lsoule

...
It looks like the # of primes found in 0-10k isn't always a good predictor of larger primes (unless the range happens to hit the arbitrarily large gaps between primes...). Any pointers here?

thanks,
Larry

Hi
A quick introduction:
I am Chris. http://primes.utm.edu/bios/page.php?id=738

I have a limited mathmatical education and find maths very hard but very interesting. If you assume you are talking to an idiot you won't be far wrong!

I have been testing the number of primes for various ks up to a few thousand for n up to 15000.

Is there any link between the size and frequency of the large gaps between primes and the distribution of the factors of k?

For example, will a k made from say 3*3*5*13*19*31 (Nicely grouped factors.) produce a 'smoother' distribution of primes (on average) than say 3*3*5*101*359 (Not so nice.)

Also:

Does including powers of numbers for the factors that make up k (eg. 3*5*5*5*19*19) affect the 'smoothness' of the distribution of the resulting primes. (Ignoring any reduced chances of finding a prime.)

Regards

Chris