Problem Ten revisited

[Harvey563]

32 bit WinXP

[rogue]

I can't do anything about a Win32 build for a while. Here is the latest source, version 1.1.0. I don't recall the changes from v1.0.0, but I think it had to do with some issues where I didn't expect the code to build on other platforms. I haven't build it on Linux, but if it does build and link, then it should run. If it doesn't, then let me know and I'll address the problem.

[rogue]

Steven found some compiler errors on Linux. I hope that they are fixed with this.

[Harvey563]

4900 through 4999 is completed. I went to * for 4914 and 4956.

I am currently sieving 5000 through 5999, and will start checking 5000 and up when the rate of elimination equals the rate of checking. Probably in a week or so.

[Harvey563]

I am through sieving, and am now checking 5000 through 5099.

[Harvey563]

completed through 5099, went to * for 5010, 5059, 5069, 5073.
taking 5100 through 5199.

[gd_barnes]

This is an interesting conjecture to work on.

Reserving 5200 thru 5299.

If preliminary estimates are correct, ETA should be ~2-3 weeks running 5 cores of a 2.9 Ghz I7 quad.

[gd_barnes]

Originally Posted by Mini-Geek

For 4981<=k<=5000 (also a 20 k block), the expected primes per k is about 7.88. That makes a 0.038% chance for a k to have no primes. That means that for every 1826 k's this size, you should have a 50% chance of having one with no primes.
This is good news: as k goes up, the chance of finding an all-composite k on any given k goes up, so the higher we go, the better the chances of it ending. Yes, the time per test, and the time per k will continue to go up, but at least we'll have better and better chances of disproving the conjecture as it goes up. (contrast this with CRUS, where each test gets longer, and the chance of a prime gets lower, making it extremely hard very quickly)

Since I've just noticed this project, I thought I would respond to an old post in this thread. I'd like to clarify a little more the last statement above because the difference between here and CRUS is not as pronounced as one might expect:

Here as you double p(k)#:
Size goes up ~2.2x.
Avg. test time for each candidate goes up ~4.5x.
The # of candidates to test goes up 2x.
Chance of each candidate being composite is increased ~2.2x.

Therefore the avg. testing time for a doubling of p(k)# goes up ~4.5x * 2 = ~9x.
Now, dividing that by ~2.2x means that the expected time expenditure for finding all composites upon a doubling of p(k)# is increased by 4x.

At CRUS as you double n:
Size goes up 2x.
Avg. test time for each candidate goes up 4x.
Chance of each candidate being prime is DEcreased 2x.

Therefor the avg. the expected time expenditure for finding a prime upon a doubling of n is increased by 4*2 = 8x.

So the bottom line is that the difficulty of finding a prime at CRUS increases twice as fast as the difficulty in finding all composites here. That's certainly less of a difference than I would have expected.

I bring this up because the doubling of candidates to test upon doubling p(k)# here makes it become difficult faster than one might expect. If this project reaches p(k)# = 10000 without being disproven, it will require a whole lot of resources to continue.

[gd_barnes]

Steven,

How come you have me reserved for k=5515 ?

How did the higher k's such as 5379, 5415, 5752, and 5977 get searched ? I'm assuming that they were obtained from some random top-5000 primes from many years ago. It's not easy to deduce them since the method that they are shown at top-5000 is different as demonstrated at the bottom of your page.

On the primes for those higher k's, you have omitted the "#" symbol.


Gary

[Harvey563]

The reservation for 5515 is a typo which I'll fix soon.

The other primes are from the top5000 list from years ago.
There is an nth prime applet on the prime pages that makes conversion fairly easy.
Thanks for the corrections!

Steven

[Harvey563]

Another option to figure out the integer value of a particular prime is to use PFGW.

Example:

pfgw -qp(5891) -f0 -od

gives

PFGW Version 3.4.8.32BIT.20110617.Win_Dev [GWNUM 26.6]

p(5891): 58171

Done.