primes to expect per k?

[roger]

I'm wondering how few n's a 'good' k should go through for 25, 50, 100 primes.

Thanks,

Roger

[VBCurtis]

Can you be more specific? Do you mean a k's first 25/50/100 primes? These numbers vary quite a bit, esp for first 25; there are k's that produce quite a few small primes, but not so many large primes (I no of no explanation for this).

It's easier to measure a k's weight/production by how many primes below n=100,000. You can count this yourself on our k<300 stats page, or read the threads about high-weight k's to see the fruit of a few members' search for the highest-weight k's around. Unfortunately, the very high-weight k's are also very large, which means LLR is slower per test. For instance, n=500k on k~3e9 took about the same amount of time as n=700k on k~100.

Weight and production of primes are not directly correlated, but they're close. Larry has a spreadsheet from over a year ago that studied this relationship (look for a thread titled something like "weight vs number of primes").

-Curtis

[roger]

Thanks, curtis

Yeah, I mean a k's first 25/50/100 primes. So far [I have been searching through small n's for 'good' k's] the best I've seen is 32 primes for 7000 n's with a 6-digit k. [worst is 8 primes for 10000 n's]

I'll have a look around, and BTW I also noticed that some k's produce many small primes and no large. That's primes for you...

Roger

[robert44444uk]

The best I have managed at 25/50/75/100 primes are 56/294/1254/3258, all for + series.

More detail:

10 primes/n=10
20/37
30/83
40/173
50/294
60/550
70/847
80/1599
90/1951
100/3258
110/4495
120/12950
130/19593
140/52310
150/122428
160/202474
170 no k found

[roger]

Robert, Thanks for the numbers, they'll come in handy for when I have something to relate to them!

Roger