Sierpinski/Riesel Base 5: Post Primes Here

[masser]

175268*5^360870-1 is prime!

[rover]

LLR tests only k*2^n▒1 numbers, so, we will do a PRP test of 171362*5^8436-1
171362*5^8436-1 is not prime. RES64: CDB0FC3DC8D8D595 Time: 4.078 sec.
The server refused your new result :
either someone else computed it already,
either the server is now configured to
work on other numbers.

[ltd]

I had the same error. It looks like the server having some problems when resheduling where short tests. It did send out the test several times.

I have checked and all result for n<10000 are in now. I will remove the "damaged" tests from the queue.

Lars

Edit:

We will see some new small tests as there have been two false positives.

[axn]

73198*5^101383-1 is prime!

Yay me!

[michaf]

Is there any educated guess on how fast we will remove candidates from now on?
Can we say: "we will probably have around xxx k's left when we reach n=200k?"

For now, every few thousand n will yield a prime, but that will not continue obviously...
Can anyone answer that with a good background in the math?

[axn]

Originally Posted by michaf

Is there any educated guess on how fast we will remove candidates from now on?
Can we say: "we will probably have around xxx k's left when we reach n=200k?"

For now, every few thousand n will yield a prime, but that will not continue obviously...
Can anyone answer that with a good background in the math?

I did some frequency count analysis (looking at how many primes were found between 2^x <= n < 2^(x+1)). Based on that, we can expect to find another 10-12 Riesel primes and 8-10 Sierpinski primes before n < 2^17 (131072). Between 2^17 and 2^18, we can expect to see another 25-30 primes.

The problem is that we are not sure whether all the primes found so far are the lowest for their repsective k's. This could throw-off the analysis a bit.

[axn]

272464*5^101667-1 is prime!

Congrats to rover

[michaf]

Originally Posted by axn1

I did some frequency count analysis (looking at how many primes were found between 2^x <= n < 2^(x+1)). Based on that, we can expect to find another 10-12 Riesel primes and 8-10 Sierpinski primes before n < 2^17 (131072). Between 2^17 and 2^18, we can expect to see another 25-30 primes.

The problem is that we are not sure whether all the primes found so far are the lowest for their repsective k's. This could throw-off the analysis a bit.

Let's just disregard any errors made on that part so far :)
Can you make a list of expected number of primes/expected number of k's left with each 2^x?

Oh, and one other thing, is there a known limit to which we can/must sieve, or will we simply not reach a point where sieving is slower than prp'ing?

Oh and, of course, congrats to rover!

[R. Gerbicz]

Originally Posted by michaf

Can you make a list of expected number of primes/expected number of k's left with each 2^x?

By a little modification of my (PARI) program: see: http://www.rieselsieve.com/forum/viewtopic.php?t=650
This is a fast program. Takes only few sec.
The only differences:

num=300;\
test=17;\
u(n,test,i)=c=exp(-w[i,2]*(n-test)*log(2)/log(5));

Because here base=5 and not base=2. And there are 300 remaining k values
and supposing that we finished the project to n=2^17 and you have to
modify the w matrix.

Supposing that all remaining k values has been tested up to 2^17=131072 (this isn't true, but some numbers has been tested up to say 200,000).
By 50% probability we can expect there will be only:

up to 2^18 expected remaining:243
up to 2^19 expected remaining:199
up to 2^20 expected remaining:164
up to 2^21 expected remaining:136
up to 2^22 expected remaining:114
up to 2^23 expected remaining:96
up to 2^24 expected remaining:81
up to 2^25 expected remaining:69
up to 2^26 expected remaining:59
up to 2^27 expected remaining:51
up to 2^28 expected remaining:44
up to 2^29 expected remaining:38
up to 2^30 expected remaining:33
up to 2^31 expected remaining:29
up to 2^32 expected remaining:25
up to 2^33 expected remaining:22
up to 2^34 expected remaining:20
up to 2^35 expected remaining:17
up to 2^36 expected remaining:16
up to 2^37 expected remaining:14
up to 2^38 expected remaining:12
up to 2^39 expected remaining:11
up to 2^40 expected remaining:10
up to 2^41 expected remaining:9
up to 2^42 expected remaining:8
up to 2^43 expected remaining:7
up to 2^44 expected remaining:6
up to 2^45 expected remaining:6
up to 2^46 expected remaining:5
up to 2^47 expected remaining:5
up to 2^48 expected remaining:4
up to 2^49 expected remaining:4
up to 2^50 expected remaining:4
up to 2^51 expected remaining:3
up to 2^52 expected remaining:3
up to 2^53 expected remaining:3
up to 2^54 expected remaining:3
up to 2^55 expected remaining:2
up to 2^56 expected remaining:2
up to 2^57 expected remaining:2
up to 2^58 expected remaining:2
up to 2^59 expected remaining:2
up to 2^60 expected remaining:1
up to 2^61 expected remaining:1
up to 2^62 expected remaining:1
up to 2^63 expected remaining:1
up to 2^64 expected remaining:1
up to 2^65 expected remaining:1
up to 2^66 expected remaining:1
up to 2^67 expected remaining:1
up to 2^68 expected remaining:1
up to 2^69 expected remaining:1
up to 2^70 expected remaining:1
up to 2^71 expected remaining:1
up to 2^72 expected remaining:1
up to 2^73 expected remaining:0

It is a little interesting, because it has got the same expected last level: 2^73, as for Rieselsieve. I thought that it will be say 2^128, because there
are so many unfinished k values.

[michaf]

Ouch... so when we get to the end of the current sieve-range, there will still be around 130 candidates left...

On another note, that would be a whopping 170 primes found! :>

[axn]

Originally Posted by R. Gerbicz

up to 2^18 expected remaining:243
up to 2^19 expected remaining:199

snip

Well it looks like your estimation matches my SWAG upto 2^18. Of course, as we hit each milestone, we'll have to redo the estimation to sync-up with reality (i.e. actual number of k's left)

Originally Posted by michaf

Ouch... so when we get to the end of the current sieve-range, there will still be around 130 candidates left...

On another note, that would be a whopping 170 primes found! :>

Let us hope that we will be really lucky and dealing with a lot less k's by then