mersenneforum.org primes to expect per k?
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 2007-04-27, 21:28 #1 roger     Oct 2006 22×5×13 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 VBCurtis     "Curtis" Feb 2005 Riverside, CA 10DF16 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 roger     Oct 2006 22·5·13 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 robert44444uk     Jun 2003 Oxford, UK 3·54 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 roger     Oct 2006 10416 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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