So I expect the PARI code to check
![$Z < p \le \max$ $Z < p \le \max$](https://dxdy-04.korotkov.co.uk/f/b/1/4/b1413a100aa316c68f2bcd10d64d5cb482.png)
, for some computed maximum.
But no one forbids checking not
![$Z<p<\max$ $Z<p<\max$](https://dxdy-01.korotkov.co.uk/f/8/6/b/86b6f6e1c09af9988426443be79cad8082.png)
, but this much
![$0<p<\max$ $0<p<\max$](https://dxdy-02.korotkov.co.uk/f/9/1/a/91a63801c9db8ca6aa061aa9105d8f6c82.png)
.
If "qrmin" is correctly calculated as the minimum valid
![$qr$ $qr$](https://dxdy-02.korotkov.co.uk/f/5/2/3/523e4ddd77f0a12cc9d42f967001497b82.png)
, then "sqrt(stop/qrmin)" seems like the correct way to get the computed maximum, but when I talk about "pmin" I'm talking about that value Z. If you're going to calculate it from qrmax, it would probably be "sqrt(stop/qrmax)", but that calculation also does not appear.
I repeat: qrmin and qrmax are set by the person at will, well, that's how I wrote the program. And from them should get
![$pmin=Z=\sqrt{10^{22}/qrmax}$ $pmin=Z=\sqrt{10^{22}/qrmax}$](https://dxdy-04.korotkov.co.uk/f/7/c/2/7c22df731434758b15355b330e87a77282.png)
and
![$pmax=\sqrt{10^{22}/qrmin}$ $pmax=\sqrt{10^{22}/qrmin}$](https://dxdy-01.korotkov.co.uk/f/4/1/e/41eecdd691842f1a2ff3173253605cf282.png)
, but I accept that pmin=0, I have the right, just add to myself work, nothing more. But of course
![$Z$ $Z$](https://dxdy-02.korotkov.co.uk/f/5/b/5/5b51bd2e6f329245d425b8002d7cf94282.png)
is not zeroed, it remains
![$Z=\sqrt{10^{22}/qrmax}$ $Z=\sqrt{10^{22}/qrmax}$](https://dxdy-04.korotkov.co.uk/f/7/7/5/775aa16d09803b0b43d79b74b5b513dd82.png)
.
So, rather, why are we not interested in eg
![$qr=22$ $qr=22$](https://dxdy-03.korotkov.co.uk/f/6/e/f/6ef05a9b18519ca059771e71ec2b687982.png)
? Which is to say, why are we only interested in
![$q \ge 13$ $q \ge 13$](https://dxdy-02.korotkov.co.uk/f/d/9/c/d9ce94740dacc76bf04fafe507c1970a82.png)
?
Because I took the conditions
![$q\ge 13, q>r, r\ge 2, q\cdot r=qr<qrmax$ $q\ge 13, q>r, r\ge 2, q\cdot r=qr<qrmax$](https://dxdy-03.korotkov.co.uk/f/6/0/4/60444b2a874c4addb45c4a1aab9a78ad82.png)
(which of
![$q,r$ $q,r$](https://dxdy-02.korotkov.co.uk/f/9/2/8/928c9473c24889309fa8b61baaa17de282.png)
to choose is greater and which is less is arbitrary, I took
![$q>r$ $q>r$](https://dxdy-04.korotkov.co.uk/f/b/9/a/b9ae56f5bdfd9f9aa62932aad2d64fdc82.png)
). With these conditions there is no way we can get
![$qr<26$ $qr<26$](https://dxdy-04.korotkov.co.uk/f/b/7/a/b7aa10a2705d7fdb0bc5accae7aaaf0482.png)
. And the condition
![$q\ge 13$ $q\ge 13$](https://dxdy-02.korotkov.co.uk/f/5/d/2/5d275fd1220d16340e56864d961b978882.png)
is due to the fact that we have already placed all the smaller primes in the pattern.
All possible variants
![$13>q>r \ge 2$ $13>q>r \ge 2$](https://dxdy-01.korotkov.co.uk/f/4/7/9/479d1e74ff1f14c1cb5e0435f03d435c82.png)
can be eliminated at once for all patterns by a single enumeration of
![$p^2$ $p^2$](https://dxdy-04.korotkov.co.uk/f/3/6/7/367612346bbcbb202f19d739190c1a9982.png)
up to
![$p<\sqrt{10^{22}/6}<4.1\cdot10^{10}$ $p<\sqrt{10^{22}/6}<4.1\cdot10^{10}$](https://dxdy-01.korotkov.co.uk/f/8/c/f/8cf9bf2897d3f027d6405e636cdbcb5382.png)
, even if one does not believe my proofs from page 140 of this thread. Or one can of course relax the conditions on qrmin and qrmax here as well.
-- 22.11.2022, 00:37 --Program:
Код:
qrall=Set([2*5,2*7,2*11,3*5,3*7,3*11,5*7,5*11,7*11]); pmin=1e9; pmax=sqrt(stop/vecmin(qrall));\\qrall - sorted vector from min to max
{forprime(p=pmin,pmax,
foreach(qrall,qr,
h=p^2*qr; nn=round(h/32); if(h>stop, qrall=setminus(qrall,[qr]); break, !ispseudoprime(nn), next);\\To accelerate, delete a value that is too large and interrupt the loop.
h=nn*32; x=h%18;
if(x==2, if(!ispseudoprime((h-2)/18) || numdiv(h+2)!=12, next);
, x==16, if(!ispseudoprime((h+2)/18) || numdiv(h-2)!=12, next);
, next;
);
if(numdiv(h-1)!=12 || numdiv(h+1)!=12, next);
print("32x=",h);
);
if(#qrall==0, break);\\If qrall is empty then exiting
)}
Estimate work time is 4h.