2007-04-27, 21:28 | #1 |
Oct 2006
2^{2}×5×13 Posts |
primes to expect per k?
I'm wondering how few n's a 'good' k should go through for 25, 50, 100 primes.
Thanks, Roger |
2007-04-27, 21:47 | #2 |
"Curtis"
Feb 2005
Riverside, CA
10DF_{16} Posts |
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 |
2007-04-27, 22:04 | #3 |
Oct 2006
2^{2}·5·13 Posts |
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 |
2007-04-28, 06:02 | #4 |
Jun 2003
Oxford, UK
3·5^{4} Posts |
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 |
2007-04-29, 04:29 | #5 |
Oct 2006
104_{16} Posts |
Robert, Thanks for the numbers, they'll come in handy for when I have something to relate to them!
Roger |
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