Excellent! I was wondering when this was going to happen. :D

Thanks guys
____________

What's so special about Sophie Germain primes? The 2p+1 definition seems kind of arbitrary. Why not 3p + 2? I can think of a few - 5 and 17, 23 and 71, etc. Or 6p + 1? 7 and 43 match that too.

I know you included links, but the only thing interesting about them is that they were once mentioned in a movie.

There seems to be no double checkers on these WUs. Why is this so?
____________

It seems fairly random. Some of min have dblchk, some don't
____________

What happens if a WU with no replication turns out to be prime? Will it then be sent for a double check?
____________

An odd thing that I've noticed is that it seems to take significantly longer (~20% longer) to process these WUs then to process pps_llr WUs that test n values >666666. Why do these tasks take longer to process than the pps tasks that are testing larger numbers? Is the algorithm different? From the original post I assumed that the WUs would only be longer than normal if a prime was found and a test of the other three forms was necessary. Just curious...

Cheers!
Alan
____________

Thanks Lennart...Wow, it is interesting that the size of k matters more than the size of the actual number being tested.

For instance, 1177*2^669246+1 took 498s to crunch

http://www.primegrid.com/workunit.php?wuid=82112380

while 16715444655*2^666670-1 took 682s to crunch on the same box.

http://www.primegrid.com/workunit.php?wuid=82113124

There are far more digits in 1177*2^669246+1 than in 16715444655*2^666670-1. It's a bit counterintuitive to me that the bigger number is faster to crunch, but I guess the llr program must take advantage of some shortcut with smaller k values?
____________

Iam missing a server status for SGPS?!
____________

Are there plans to have a server status section for the Sophie Germain prime search?

Just wondering
____________

Rytis,

I see the stats on http://www.primegrid.com/stats_sgs_llr.php

Question on the totals.

In the stats-page totals are missing for the "total tasks" and "done tasks" Doing a quick count I got to 218687 total tasks, of which 25% appears to be done. According to the stats we will be done within a few weeks.

In the initial post it is stated "candidates remaining: 34,190,344". If that is true this will run for a few months.

Which interpretation is correct?

Alexander

Rytis: The deadline with 4 days is very short, can you extend it to 7 days?
____________

@Alan: Actually the factor k is also a multiplicative time factor to compute the result with the LLR algorithm. The complexity is about k * complexity of prime-testing of (2^n-1).

cool:) Thanks Bruno!
____________

is this search done once we've crunched the remaining units? or will it be extended to other n values?

It is when the sophie germain prime has been found. So finding a prime k*2^n-1 where k*2^(n+1)-1 is prime also.

So when a prime is found in SGS, is it automatically tested to see if it fits into the full SGS? I see posts in here that people post their prime then someone tests it.

I found one
7555140078885*2^666666-1


____________
My lucky numbers are 121*2^4553899-1 and 3756801695685*2^666669±1

So how do we know if it's a twin?

Iam missing the digits view in subproject status...
____________

Sophie Germain Prime Search
...
We'll be searching the form k*2^n-1. If it is prime, then we'll check k*2^n+1, k*2^(n-1)-1, & k*2^(n+1)-1.

Here are some stats for the search:
...
candidates remaining: 34,190,344

Probability of one or more significant pair = 80.1%
Probability of one or more SG = 66.7%
Probability of one or more Twin = 42.3%

If someone with Intel I7 2600K could test a few units with and without HT?

I'm running this on a Intel i7 2600k with HT. :-)

What info are you looking for?

What clock, stock or OC?

stock with temps around 60C

I have not attempted to oc yet; might do that this weekend.

Ok, thanks for that information. Interesing, what time would be on 4.0/4.5 GHz.

Hi

Sorry for my poor english. I m french I a prefered lear women than other language ...

I'm not mathemetician but inbformatician*
My goal is to done max computer power to the scientist not to do heir jobs

I 'm not able to create a sieve but give me the idea and I make the max powerful application(I try...)
Interested by twin( I have a twin brother)
I download TPS code and I don't belive it:
35 pages of code,1 or 2 G of RAM, X G of HD space and year of cpu

To do a Sophie Germain search you need 10 liines of code, no ram,no hd,

You(mathematicians) find that a Sophie number is can be write 6k-1
So we only have to compute all caandidas verify if is_Prime
add 2 and verify the primarity of the new walue

You don't realaese the importanec ,for computer,of this
We can write a stieve 10 times more speed hat Erasthotèène!!!!!



the naif code ot search twin smaller then 1 000 000 is:


B:=1000000;
A:=5; // we begin with 11 a:= (6 *1) -1
repeat
A:= A+6;
If Is_Prime (A) then
if Is prime(A+2) then
begin
Inc(Offset)
twins[offset]:=A;
end;
until A>B;

With this sieve no first attemp to eliminate candidat,
no RAM, no Hd direcly the number of candidats. B div 6 =166667 primeity tst
You can make the resarch on a Phone(Idea to BOINC)


AND DON'T FORGET

it' the naif code : it's easy to do speeder


What is the WR for Twin? 120 000 Digits?

Jerôme

Hi
I a prefered lear women than other language ...

Hi,

Your code could be written in full to give a useful routine for finding either primes or twin primes for the lower numbers (up to say 10^8) with reasonable speed, higher if you are patient, but the catch is the "Is_prime" subroutine.

It would be something like :

Is_prime (a)

Var
file : primes.CSV {2,3,5}
file twins.CSV {2:3,3:5}

Begin
c :=a-1
d:=a+1
Is_primec :=1
Is_primed :=1
open primes
while not EOF repeat
read test
sqr := sqrt(a+1)
while test < sqr do
begin
if mod(c,test) = 0 then Is_primec :=0
if mod(d,test) = 0 then Is_primed
end
if Is_primec and Is_primed <> 0 then next test
else end
If Is_primec = 1 then append primes(","c)
if Is_primed = 1 then append primes(","d)
if Is_primec and Is_primed = 1 then append twin (","c":"d)
end


This tests both a-1 and a+1 for primality and twin primality and saves the result to the file if either is prime, the same prime file being reused in the testing. The files are .CSV files.

The program is not of course complete, but it does show the idea.

The problem is that as we get to very big numbers (10^100000) the files would be MASSIVE, many million tersbytes in length, and the tests would take hundreds of years to complete even on the fastest PC.

The idea could however be useful as a student code example. About 20 years ago when I did my BComp degree we were given an assignment in optimisation using Turbo Pascal, 10 or 20% of the marks were based on the 10 percentile placing in the class when the code was run to 1,ooo,ooo on the lecturers PC. The slowest tested every number (including even ones), others tested every odd number, the faster tested at 6n+_1. Testing for divisibility by all numbers, just odd numbers and only primes gives added speed variation. Many other optimisations are possible but they will never solve the problems for extreme times with the size of numbers PG uses.

It could be written in any language but Java would be good and allow easy graphic displays of the population densities of the resuts for example.
____________
Member team AUSTRALIA
My lucky number is 9291*2^1085585+1

Among Newly reported primes there are some 333333. How comes?
65516468355*2^333333+1
65516468355*2^333333-1

This is also listed under Other significant primes.

As you are searching for Sophie Germain Prime, I wonder if you could give me some Sophie Germain Prime between 2^4096 ~ 2^32768. All I can found on the internet either too large or too small for me. I've got two in the site primes.utm.edu. 18458709× 2^32611- 1 and 470943129×2^16352- 1 is what I have at hand. I need another two at least. The more, the better. I would be very appreciate is you could give me some. Thank you!

As you are searching for Sophie Germain Prime, I wonder if you could give me some Sophie Germain Prime between 2^4096 ~ 2^32768. All I can found on the internet either too large or too small for me. I've got two in the site primes.utm.edu. 18458709× 2^32611- 1 and 470943129×2^16352- 1 is what I have at hand. I need another two at least. The more, the better. I would be very appreciate is you could give me some. Thank you!

As you are searching for Sophie Germain Prime, I wonder if you could give me some Sophie Germain Prime between 2^4096 ~ 2^32768. All I can found on the internet either too large or too small for me. I've got two in the site primes.utm.edu. 18458709× 2^32611- 1 and 470943129×2^16352- 1 is what I have at hand. I need another two at least. The more, the better. I would be very appreciate is you could give me some. Thank you!

PrimeGrid is not your (nor anyones) personal prime generating project. Since the numbers are really small you should easily be able to find them yourself. Or else you could always start your own distributed computing effort to find them.

As you are searching for Sophie Germain Prime, I wonder if you could give me some Sophie Germain Prime between 2^4096 ~ 2^32768. All I can found on the internet either too large or too small for me. I've got two in the site primes.utm.edu. 18458709× 2^32611- 1 and 470943129×2^16352- 1 is what I have at hand. I need another two at least. The more, the better. I would be very appreciate is you could give me some. Thank you!

Go to http://primes.utm.edu/primes/search.php

Put Sophie Germain (p) in the "Text Comment" textbox

Select "All verified primes" radio button.

Enter 500 in "Maximum number of primes to output "

Select output style as "Text (printable)"

62102 18131*22817#-1 9853 L 2000 Sophie Germain (p) 62119 18458709*2^32611-1 9825 CK 1999 Sophie Germain (p) 62470 847067781*2^30790-1 9278 L4 2003 Sophie Germain (p) 62708 415365*2^30052-1 9053 g141 1999 Sophie Germain (p) 62920 60940331*2^29439+1 8870 g136 2002 Sophie Germain (p) 63182 23345*2^28601+1 8615 g171 2003 Sophie Germain (p) 63688 18482685*2^27182-1 8190 g206 2001 Sophie Germain (p) 63979 22717075*2^26000+1 7835 x11 2001 Sophie Germain (p) 64316 161193945*2^25253-1 7611 g137 2001 Sophie Germain (p) 64461 121063995*2^25094-1 7563 g120 2001 Sophie Germain (p) 64462 120136023*2^25094-1 7563 g120 2001 Sophie Germain (p) 64540 1051054917*2^25000-1 7535 g52 2000 Sophie Germain (p) 64651 626711007*2^24712-1 7448 g144 2001 Sophie Germain (p) 64652 885817959*2^24711-1 7448 g217 2001 Sophie Germain (p) 64664 1392082887*2^24680-1 7439 g137 2000 Sophie Germain (p) 64940 14516877*2^24176-1 7285 CK 1999 Sophie Germain (p) 65097 471631965*2^24000-1 7234 g298 2002 Sophie Germain (p) 65300 72021*2^23630-1 7119 g0 1998 Sophie Germain (p) 65352 325034895*2^23472-1 7075 g205 2000 Sophie Germain (p) 65353 1297743285*2^23470-1 7075 g205 2001 Sophie Germain (p) 65372 1186447755*2^23457-1 7071 g144 2000 Sophie Germain (p) 65386 613702635*2^23457-1 7071 g144 2000 Sophie Germain (p) 65954 1354921707*2^23005-1 6935 g141 2001 Sophie Germain (p) 65961 224420829*2^23003-1 6933 g141 2000 Sophie Germain (p) 65962 1579278645*2^23000-1 6933 g141 2000 Sophie Germain (p) 65963 255346125*2^23002-1 6933 g141 2000 Sophie Germain (p) 66932 1654523577*2^20304-1 6122 g137 2000 Sophie Germain (p) 67297 29553033*2^19990-1 6026 g141 1999 Sophie Germain (p) 67337 184748277*2^19912-1 6003 g206 2000 Sophie Germain (p) 67393 31467345*2^19761-1 5957 g141 1999 Sophie Germain (p) 67556 2375063906985*2^19380-1 5847 IJ 1996 Sophie Germain (p) 67687 276311*2^19003+1 5726 g23 1998 Sophie Germain (p) 68901 3382599*2^17075-1 5147 g27 1999 Sophie Germain (p) 68910 757321845*2^17051-1 5142 g141 2000 Sophie Germain (p) 68911 454332273*2^17051-1 5142 g141 2000 Sophie Germain (p) 68913 338234883*2^17050-1 5142 g141 2000 Sophie Germain (p) 68924 421907295*2^17029-1 5135 g141 2000 Sophie Germain (p) 69006 48859797*2^17000-1 5126 g141 1999 Sophie Germain (p) 69029 92305*2^16998+1 5122 g14 1998 Sophie Germain (p) 69177 8069496435*10^5072-1 5082 D 1995 Sophie Germain (p) 69956 "2^16383-2^16319-1+2^63*(floor(2^16254*Pi)+50814484)" 4932 c9 2003 ECPP, Sophie Germain (p) (**) 70052 470943129*2^16352-1 4932 IJ 1995 Sophie Germain (p) 70144 157324389*2^16352-1 4931 IJ 1995 Sophie Germain (p) 70596 12359*2^15405+1 4642 g122 2000 Sophie Germain (p) 70726 11263*2^15318+1 4616 g122 2000 Sophie Germain (p) 70899 5415312903*10^4526-1 4536 D 1994 Sophie Germain (p) 70974 48101037*2^15005-1 4525 g141 2000 Sophie Germain (p) 70975 28671705*2^15005-1 4525 g141 2000 Sophie Germain (p) 70983 44941785*2^14999-1 4523 g141 2000 Sophie Germain (p) 71633 10211*2^13491+1 4066 g122 2000 Sophie Germain (p) 71818 1468358892*10^4003-1 4013 D 1994 Sophie Germain (p) 71930 1883535*2^13133-1 3960 g141 1999 Sophie Germain (p) 72021 224529135*2^12648-1 3816 g2 1998 Sophie Germain (p) 72204 "2^12287-2^12223-1+2^63*(floor(2^12158*Pi)+7425765)" 3699 c9 2003 ECPP, Sophie Germain (p) (**) 72206 5293*2^12270+1 3698 g122 2000 Sophie Germain (p) 72358 15614233635*10^3529-1 3540 D 1994 Sophie Germain (p) 73717 27692175*2^10409-1 3141 g141 1999 Sophie Germain (p) 73799 22155*2^10164-1 3065 g35 1998 Sophie Germain (p) 73818 5546061*2^10113-1 3052 g155 1999 Sophie Germain (p) 74523 47013511545*10^2999-1 3010 D 1993 Sophie Germain (p) 74635 4627755*2^9878-1 2981 g2 1998 Sophie Germain (p) 74676 196949037*2^9752-1 2944 g141 1999 Sophie Germain (p) 75031 15489885*2^8906-1 2689 g27 1999 Sophie Germain (p) 75362 1746052308*10^2581-1 2591 D 1993 Sophie Germain (p) 76938 22714209*2^8087-1 2442 g14 1998 Sophie Germain (p) 77053 9303607*2^8004+1 2417 g2 1998 Sophie Germain (p) 77069 10497687*2^8000-1 2416 g210 2001 Sophie Germain (p) 77900 4837*2^7574+1 2284 DM 1996 Sophie Germain (p) 78229 2667027*2^7389-1 2231 CK 1999 Sophie Germain (p) 78877 8980569*2^7179-1 2169 g14 1998 Sophie Germain (p) 78910 14096107*2^7168+1 2165 CR 1997 Sophie Germain (p) 78911 12271975*2^7168+1 2165 CR 1997 Sophie Germain (p) 78912 12259585*2^7168+1 2165 CR 1997 Sophie Germain (p) 79224 6341*2^7039+1 2123 g34 1998 Sophie Germain (p) 79282 21063042*10^2110-1 2118 D 1993 Sophie Germain (p) 79363 20114275*2^7000+1 2115 CR 1997 Sophie Germain (p) 80195 2926924*10^2032+1 2039 D 1992 Sophie Germain (p) 82573 736320585*2^6194-1 1874 g95 1998 Sophie Germain (p) 82608 713851138*10^1854+1 1863 D 1990 Sophie Germain (p) 82771 337047945*2^5999-1 1815 g210 2001 Sophie Germain (p) 82796 39051*2^6001-1 1812 K 1986 Sophie Germain (p) 84026 89687295*2^5001-1 1514 g38 1998 Sophie Germain (p) 84031 6238665*2^5004-1 1514 g14 1998 Sophie Germain (p) 84032 67621539*2^5000-1 1513 g158 1999 Sophie Germain (p) 84033 61022115*2^5000-1 1513 g158 1999 Sophie Germain (p) 84034 110266875*2^4999-1 1513 g158 1999 Sophie Germain (p) 84037 9769767*2^5001-1 1513 g158 1999 Sophie Germain (p) 84041 5004615*2^5001-1 1513 g158 1999 Sophie Germain (p) 84043 4133481*2^5001-1 1513 K 1988 Sophie Germain (p) 87360 81127*2^4350+1 1315 g14 1998 Sophie Germain (p) 87388 531667*2^4346+1 1315 g14 1997 Sophie Germain (p) 87838 6206682*10^1300-1 1307 CR 1997 Sophie Germain (p) 88877 296385*2^4251-1 1286 Z 1989 Sophie Germain (p) 89731 53373*2^4203-1 1270 Z 1989 Sophie Germain (p)

We'll be searching the form k*2^n-1. If it is prime, then we'll check k*2^n+1, k*2^(n-1)-1, & k*2^(n+1)-1.

Will the additional tests be done manually, or in the same workunit, so that a WU with a prime is four times as long as a normal WU?

You will check k*2^n-1 and if prime you will also search k*2^n+1

We will search all primes externally on PG server for k*2^(n-1)-1, & k*2^(n+1)-1

A prime number p is called a Sophie Germain prime if 2p + 1 is also prime.

I've already found that the largest known primes of this form is
648309*2^148311+1 - Cunningham chain 2nd kind (2p-1)
648309*2^148310+1 - Cunningham chain 2nd kind (p)

44652 and 43058 digits only...
____________

Okay, why the pair of primes (p; 2p+1) has its own name - Sophie Germain primes,
but the pair of primes (p; 2p-1) hasn't, it has only the general name "Cunningham chain of the second kind of lehgth 2" ?

Do we have a plan to establish the search of the largest pair of primes (p; 2p-1) just as Sophie Germain Prime Search attempts to find the largest pair of primes (p; 2p+1)?

If a prime p is the Proth number, p = k*2^n+1,
2p-1 is the Proth number too: 2p-1 = k*2^(n+1)+1

I guess the pair of primes
648309*2^148311+1 - Cunningham chain 2nd kind (2p-1)
648309*2^148310+1 - Cunningham chain 2nd kind (p)
is small enough (44652 and 43058 digits) and there is a sense try to renew the world record. What do you think about that?
____________

For every SGS prime, no matter whether the +1 form is prime or not we test both the k*2^(n-1)-1 and k*2^(n+1)-1 forms on the server. Here is the final form of the data in our science table for a recent SGS prime:

1054899866865*2^1290000-1 is prime! Time : 2542.378 sec.
1054899866865*2^1290000+1 is not prime. Proth RES64: B0CF6CED1998C23F Time : 2498.885 sec.
1054899866865*2^1289999-1 is not prime. LLR Res64: 32BFA46352FDCC7C Time : 2311.508 sec.
1054899866865*2^1290001-1 is not prime. LLR Res64: 21D0038F7A5148BA Time : 2277.467 sec.

We'll be searching the form k*2^n-1. If it is prime, then we'll check k*2^n+1, k*2^(n-1)-1, & k*2^(n+1)-1. We are able to do this because a quad sieve was performed for this search. This sieve ensured that k*2^n-1, k*2^n+1, k*2^(n-1)-1, & k*2^(n+1)-1 did not have any small prime divisors. The opportunity to find SG's and Twins in the same sieve file is appealing. However, we "expect" to find a Sophie Germain prime first.

2618163402417*2^1289999 - 1 has factor 5

[...] how is it possible that k*2^(n-1)-1 has such a small factor (5 is small!)?

2618163402417 mod 5 = 2
2^1289999 mod 5 = 2^(1289999 mod 4) mod 5 = 2^3 mod 5 = 3 [Fermat's little theorem]
2*3-1 = 5

Michael, I am not sure it makes sense. The quote "The opportunity to find SG's and Twins in the same sieve file is appealing" is not very relevant if you use "OR - OR" rather than "AND - AND", because then for most of the candidates, in reality, there would be (very often) just a single chance (not three chances) for a "pairing".

I thought we were indeed skipping a lot of SGS pairs because we insisted on having three chances for every prime found.

But someone who knows precisely how the quad sieve is supposed to work, and what k values were in fact quad sieved for 1290000, will surely give an authoritative answer soon.

/JeppeSN

SG pair is a Cunningham chain of length n=2.

How does one maximize their chances of success of finding one? Anyone who pondered about this question for more than a moment would realize that one would want to sieve for chains of length n+1, then check the middle survivor (because this is a computationally expensive check) and then have double chances of completing the chain.

For larger n values, one can improve slightly more; e.g. for a chain of length n=6, one can sieve for length n+2, then check the middle 4 elements {c(i),c(i+1),c(i+2),c(i+3)} and if successful, proceed to checking c(i-1),c(i+4); if one of them is prime use the last chance, and if both are prime, one already has a CC-6 and still a minuscule chance of CC-7 and CC-8.

So, notwithstanding that this SG pair was found (congratulations!) and that it would not have been found if quad sieving was done correctly, -- the fact is that over the same time/effort you would have found perhaps two SG pairs (different from this one, of course) and/or would have found the first of the two already a year ago.

SG pair is a Cunningham chain of length n=2.

How does one maximize their chances of success of finding one? Anyone who pondered about this question for more than a moment would realize that one would want to sieve for chains of length n+1, then check the middle survivor (because this is a computationally expensive check) and then have double chances of completing the chain.

For larger n values, one can improve slightly more; e.g. for a chain of length n=6, one can sieve for length n+2, then check the middle 4 elements {c(i),c(i+1),c(i+2),c(i+3)} and if successful, proceed to checking c(i-1),c(i+4); if one of them is prime use the last chance, and if both are prime, one already has a CC-6 and still a minuscule chance of CC-7 and CC-8.

So, notwithstanding that this SG pair was found (congratulations!) and that it would not have been found if quad sieving was done correctly, -- the fact is that over the same time/effort you would have found perhaps two SG pairs (different from this one, of course) and/or would have found the first of the two already a year ago.

I have not checked how TwinGen is coded (and more importantly how was it actually applied), but NewPgen (see source here) proceeds by iterating over a prime generator, finding the modular exponent 2^n mod p (or (1/2)^n mod p for some sieving modes) and then removing k values for all requested composite candidates for each of the four variations (there is no room for "OR"s in that algorithm; if any of the four derivative forms k*2^(n+x)+c (where x and c are some pertinent subset of -1,0,1, ...as well as some higher x>1 for CC sieving) is divisible by p, then k is struck out; the bitmask/sparse-array structure for all prior k values does not have any counters of strikeouts or similar - only 1 or 0 for each k). NewPgen has some excellent heuristics for managing the large bit arrays and switches between when the initially huge input range collapses, but it does manage single bits; no second chances (say, 3 out of 4) are given - the latter can only be arranged by external scripting; it's not hard even if a bit tedious.

TwinGen page is quite informative on multi-sieve principles, and (I quote) "The decision criteria and discussion is more than can be easily typed into an introductory web page."

But had it been a quad sieve, it is possible that the k values would have been too high for LLR to test it efficiently and/or the sieving range would have been too large to effectively manage. /speculation

The next Challenge is the SGS LLR with the challenge being held for 1 day. Is this misprint or are we just having a crunch fest of the fastest computers. Maybe I am really thick but 11 days seems more of a contest for the proletarian as myself, to participate in. A one day challenge is not very much to crunch unless you have a Super. Hmmm, how much are those going for, wonder if I can get a lease, or lease time? LOL

Hi,

is this the only project to search for twin-primes or are there other projects on PrimeGrid that specifically look for them?

Thanks and cheers,

Chris

Thank you Michael for the answer.

That is what I figured.

Thanks,

Chris

Thanks Michael, just the thing to OC for.
____________
GPU drivers

Out of curiosity:

All new (e.g.,) GFN-15 primes are reported on the message boards, but new primes found in the SG search are not. What is the reason for this? Are they too numerous, or are they deemed uninteresting?

I'm not critical, just curious.

>They are reported

But not in the "Sophie Germain Prime Search" forum, sticky thread style, right?

But rather, I presume, under "Primegrid Primes by Project".

I was curious why some types of primes get a sticky thread whereas others don't. (It is not a terribly important question, as you call tell.)

OK, thanks guys, good to know.

Sophie Germain Prime Search
...
We'll be searching the form k*2^n-1. If it is prime, then we'll check k*2^n+1, k*2^(n-1)-1, & k*2^(n+1)-1. We are able to do this because a quad sieve was performed for this search. This sieve ensured that k*2^n-1, k*2^n+1, k*2^(n-1)-1, & k*2^(n+1)-1 did not have any small prime divisors. The opportunity to find SG's and Twins in the same sieve file is appealing....

Sophie Germain Prime Search
...
We'll be searching the form k*2^n-1. If it is prime, then we'll check k*2^n+1, k*2^(n-1)-1, & k*2^(n+1)-1. We are able to do this because a quad sieve was performed for this search. This sieve ensured that k*2^n-1, k*2^n+1, k*2^(n-1)-1, & k*2^(n+1)-1 did not have any small prime divisors. The opportunity to find SG's and Twins in the same sieve file is appealing....

Have I understood this correctly please

You eliminated a k, n combo at the sieving stage if ANY ONE of the four targets was found to be composite?

Similarly, the last time a twin prime was found, it started from the number:

The quad sieve must be broken!

For each of 30 recent primes found in this project, call them a, so:

I don't know exactly how it works -- but I know I would NOT want it to work they way you're suggesting.

The way it SHOULD work is that as long as (a) is not factored out, the candidate should stay in the sieve if ANY of (x), (y), or (z) is also not factored out. That way you have the greatest chance of finding a twin or a Sophie. If you required all three to not have any factors, you would eliminate most of the actual twins or Sophies from the sieve, no?

It doesn't surprise me that you're finding that one of x, y, or z always has small factors. I'd be surprised if they didn't.