other conjectures

[kar_bon]

For the problem 49 there's also an overview here.
I've updated up to k=500 but this should be done later in the Wiki, because the current search ranges are only available there.

[sweety439]

Originally Posted by kar_bon

For the problem 49 there's also an overview here.
I've updated up to k=500 but this should be done later in the Wiki, because the current search ranges are only available there.

You have the twin prime (k*2^n-1 and k*2^n+1) and Riesel primes for two consecutive n (k*2^n-1 and k*2^(n+1)-1), but no Proth primes for two consecutive n (k*2^n+1 and k*2^(n+1)+1), can you add the last?

[storm5510]

Originally Posted by sweety439

You have the twin prime (k*2^n-1 and k*2^n+1)...

Curious. Are you running these concurrently? What I mean is skipping from -1 to +1 and back again after incrementing n.

[sweety439]

Originally Posted by kar_bon

For the problem 49 there's also an overview here.
I've updated up to k=500 but this should be done later in the Wiki, because the current search ranges are only available there.

This page is only for the twin case and the Riesel case, for the Sierpinski case, see http://harvey563.tripod.com/cunninghams.txt

An interesting one is k=279, there is no known twin prime (k*2^n-1 and k*2^n+1), neither known 1st kind Sophie-Germain prime/Cunningham chain (k*2^n-1 and k*2^(n+1)-1) or known 2nd kind Sophie-Germain prime/Cunningham chain (k*2^n+1 and k*2^(n+1)+1)

Twin prime: CK=237
1st kind Sophie-Germain prime/Cunningham chain: CK=807
2nd kind Sophie-Germain prime/Cunningham chain: CK=32469

[KEP]

There is currently work in progress, for the Twin Conjecture, for base 2, where the 9 k's are being sieved for n=1 to n=100M. Mr. Bitcoin, BOINC (YOYO) and me, is currently sieving to p=10P and hopefully farther than that. There is currently 1,129,099 pairs remaining. I expect that to be reduced to maybe as little as 700,000 or less than 700,000, once we reach p=10P. Do not redo or overtake our effort, since we are much better off, working together - compared to competing with each other

N=100M is current max and if I live to see the exhaustion of these test range, I'll sure not start up an even higher effort for larger than 100M n's

[KEP]

I have for the past four days, finally cracked the logic needed to build a Sophie Germain conjecture sieve file. The sievefile is currently sieved to p=100e9 and has 15,241,723 terms remaining for the 32 sequences. My goal is to complete sieving to p=1000e9 (1T) and then before continuing ever higher with the sieving, I'll remove the candidates that PG has factored for us. Currently remaining minimum n=67 and maximum n=99,999,979.

Due to a seperate sieve for n=100,000,001 - it can be said for sure, that the 2 candidate k's that had n=100,000,000 remaining at p=10e9, no longer needed that n to be included in the sievefile, since neither n=99,999,999 and n=100,000,001 excisted for any of the 2 k's that had n=100,000,000 remaining. So the reported minimum and maximum is the actual minimum and maximum n for n=1 to n=100,000,000.

DO NOT start up your own effort of Sophie Germain, fixed k variable n search, since it requires some logic to do the initial work correct - logic you may not have due to inexperiency. BOINC is not applicable for sieving Sophie Germain sievefile - due to the amount of candidates remaining - eventually the matter might be a whole different - but for now it is a manual labor and eventually I might place a call out for whilling ressources, to help push the sieve and once (if) LLR2 gets working at SRBase, the offer will be for BOINC to test the candidates ready to test.

Just like with the Twin Conjecture, if I live to see the exhaustion of the testrange (n=1 to n=100M) I sure will not start up another range

[rogue]

Originally Posted by KEP

I have for the past four days, finally cracked the logic needed to build a Sophie Germain conjecture sieve file. The sievefile is currently sieved to p=100e9 and has 15,241,723 terms remaining for the 32 sequences. My goal is to complete sieving to p=1000e9 (1T) and then before continuing ever higher with the sieving, I'll remove the candidates that PG has factored for us. Currently remaining minimum n=67 and maximum n=99,999,979.

Due to a seperate sieve for n=100,000,001 - it can be said for sure, that the 2 candidate k's that had n=100,000,000 remaining at p=10e9, no longer needed that n to be included in the sievefile, since neither n=99,999,999 and n=100,000,001 excisted for any of the 2 k's that had n=100,000,000 remaining. So the reported minimum and maximum is the actual minimum and maximum n for n=1 to n=100,000,000.

DO NOT start up your own effort of Sophie Germain, fixed k variable n search, since it requires some logic to do the initial work correct - logic you may not have due to inexperiency. BOINC is not applicable for sieving Sophie Germain sievefile - due to the amount of candidates remaining - eventually the matter might be a whole different - but for now it is a manual labor and eventually I might place a call out for whilling ressources, to help push the sieve and once (if) LLR2 gets working at SRBase, the offer will be for BOINC to test the candidates ready to test.

Just like with the Twin Conjecture, if I live to see the exhaustion of the testrange (n=1 to n=100M) I sure will not start up another range

For SGS, wouldn't it be faster to sieve with fixed n and variable k? I can't imagine that it would be hard to implement such a sieve in the mtsieve framework.

[pepi37]

Originally Posted by rogue

For SGS, wouldn't it be faster to sieve with fixed n and variable k? I can't imagine that it would be hard to implement such a sieve in the mtsieve framework.

Can you make it?
Or will you? :)

[rogue]

Originally Posted by pepi37

Can you make it?
Or will you? :)

I could, but I would like to know if there is another program that sieves these terms. If so then I can see how something I write compares.

[KEP]

Originally Posted by rogue

For SGS, wouldn't it be faster to sieve with fixed n and variable k? I can't imagine that it would be hard to implement such a sieve in the mtsieve framework.

In most cases it most likely will. However, there is for the SG conjecture, only 32 k's remaining. So we would sieve a lot of unnescessary k's and we would have to repeat the testing 100,000,000 times to cover all n. I have no means to test if handeling 100M n files and combining the candidates remaining into 1 sievefile, from wich unneeded k's is removed, is actually faster than sieving all 32 k's using srsieve (tried srsieve2, but it crashed when switching to generic sieve) and then switch to sr2sieve, when done with srsieve. It appears that sieving using srsieve,remove_non_SG_pairs,continue_sieve_using_sr2sieve approach is taking about 4 to 6 CPU weeks on an i5-4670@3.4GHz. So in other words, in average at least 27.55 to 41.33 n's would have to complete sieving each second (maybe even more than that).

What has made this extremely difficult is that we have a fixed k/variable n approach due to the conjecture stating that k=807 is the smallest conjectured k, proven to never produce a SG prime for any n. So to prove that conjecture, we in other words have to prove that k: 39, 183, 213, 219, 273, 279, 333, 351, 387, 393, 399, 417, 429, 471, 531, 543,
561, 567, 573, 591, 597, 603, 639, 681, 687, 693, 699, 723, 753, 759, 771 and 795 is in fact having a prime. We are not interested in any other k's and due to the short range of k's, sieving to optimal sieve depth for fixed n, would be a nightmare as n climbs in value.

Just like with the twin conjecture, I never really found a program that could greatly outdo the use of srsieve and later on sr2sieve. There is just not (as far as I know) a really good sieve for Twins and SG primesearch, for fixed k and variable n or sequence of k's and variable n.

[KEP]

Originally Posted by rogue

I could, but I would like to know if there is another program that sieves these terms. If so then I can see how something I write compares.

Sieving 32 sequences using sr2sieve, for an input file containing 15,241,723 terms and sieving the range 100G to 1T, sieves in average p=420,000 per core and removes a factor every 1.75 CPU/seconds.