So which k do you think will be the next to fall and when?

[vjs]

Hey guys and gals just thought I'd bring back the old guessing game of when do you think we will find the next prime and for which k????

Here is the current test density for the remaining k's

k Density (remaining)
10223 0.1716
19249 0.0624
21181 0.1470
22699 0.0602
24737 0.1553
33661 0.1461
55459 0.2055
67607 0.0518

List of found primes by increasing n.


1st k= 46157 n= 698207
2nd k= 44131 n= 995972
3rd k= 65567 n=1013803
4th k= 69109 n=1157446
5th k= 54767 n=1337287
6th k= 4847 n=3321063
7th k= 5359 n=5054502
Secondpass level n=6800000
8th k= 28433 n=7830457
9th k= 27653 n=9167433
Firstpass level n=11800000

[vjs]

I'll be the first to respond...

Since I always root for the underdog

k=67607 in firstpass around n=12.3M to 12.5M

My second choice

k=55459 in secondpass around n=7.2M to 7.4M

[tqft]

24737

The n my comp is chewing on right now

[vjs]

tqft wow now that's optimistic

[tqft]

vjs,

you know the numbers better than me.

If we weren't optimistic we would be focussed on how to pass some of the k/n pairs to our grandchildren to complete processing.

[vjs]

I'm certain that that is not going to to happen not going to happen alot of the low density k's have been removed. New processors are coming out all the time, it wasn't very long ago when the thought of testing n's>10M was very daunting, at this point it's no big deal.

[Joe O]

19249 soon!

[Sceptic]

19249 soon!
He he... How did you know? Educated guess? :thumbs:

Sceptic

[vjs]

Inside info, Joe knows exactly where each prime is he just likes to keep us guessing. Or at least thats what he tells me. :rotfl:

His last prediction was pretty close too.

[Mystwalker]

Inside info, Joe knows exactly where each prime is he just likes to keep us guessing. Or at least thats what he tells me. :rotfl:

His last prediction was pretty close too.
Sounds to me like "JoeOFacts" (similar to BruceSchneierFacts resp. ChuckNorrisFacts). ;)

[engracio]

Alright Joe, what do you know? Who is next? Let the guru speak.:D Came the closest last few primes. 55459 is my guess.

e

[Velociraptor]

Just a question.

Is the n increasing by one?

If your wouldnt it be better to generate the next n by random?

[vjs]

good question, but something a little difficult to answer.

First, Yes the n increases by one each time... however we know in advance which n's will not be prime so we don't test those. What this mean is that the n may increase more than 1 each time.

Second, no it would not be benifital to randomly choose n's for two reasons. Why? because the larger n's take longer to test in addition the larger the n the smaller the chance of it being prime.

So, long and steady start with the smallest work our way to larger n's.

[jasong]

Just a question.

Is the n increasing by one?

If your wouldnt it be better to generate the next n by random?
I think I can explain a little better(which is quite unusual, if you know me).

When they started, they had Seventeen k's and infinite possibilities for which n's could yield prime. The smartest thing is to start with the shortest possible tests, which happen to be the lowest untested n's for that k. The problem is that, as the n-value increases by 50%, the time to do a test doubles. The partial solution is called sieving. Basically, you pick a range of n(say, 1 to 50 million) and you test for small factors. "Small" being a relative term. I don't know the statistics for Seventeen or Bust Sieving, but over at a similar project we're sieving n's up to 20 million, and at least 299/300ths of the possibilities have had a factor found for them, which means that progress is about 300 times as fast as it would have been if we hadn't tested for small factors.

[Joh14vers6]

Here is the current updated test density for the remaining k's

k Density (remaining)
10223 0.1824
21181 0.1554
22699 0.0643
24737 0.1669
33661 0.1554
55459 0.2203
67607 0.0553

List of found primes by increasing n.


1st k= 46157 n= 698207
2nd k= 44131 n= 995972
3rd k= 65567 n=1013803
4th k= 69109 n=1157446
5th k= 54767 n=1337287
6th k= 4847 n=3321063
7th k= 5359 n=5054502
Secondpass level n=6970000
8th k= 28433 n=7830457
9th k= 27653 n=9167433
10th k= 19249 n=13018586
Firstpass level n=13330000

[Tallbill]

I still cant come close to understanding the math behind this. But hey, I'll keep crunching!