I noticed also that it can save some time (including in many cases an ispseudoprime check) if you look at
at the very start, and continue testing only if
. That is enough to verify that the
of
is not divisible by 2 or 3, and that
. (I'm fairly sure I have the right values for
, after stepping through a handful of cases.)
I question these 4 values of yours. At least 9 and 10. Let's do the math:
,
- not 1 or 5!
,
- not 1 or 5!
,
- ok.
,
- ok.
The case
is excluded because 3 is already in 18 and the remaining unknown prime cannot be a 3 (then it would increase the power of 3 here and the divisors would definitely not be 12) and cannot have a remainder 3 modulo 6 (there is only one prime, 3 itself, which is already excluded).
No decisions are missed, but the work is half as slow as possible.
But: we don't need
if they get further than 7 from
, i.e. 400-408 is unnecessary, as is 424-431.
This leaves only 409-423 modulo 576 acceptable:
Код:
? for(i=0,576-1, n=round(i/32); h=32*n; x=round(h/18); if(abs(h-i)<8 && (n%6==1 || n%6==5) && (x%6==1 || x%6==5), print1(i,", ")))
409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423,
Of all these, can actually be found in
only such::
Код:
? m=vector(576); forstep(p=1,#m,2, if(p%6==3, next); forstep(qr=1,#m,2, if(qr%6==3, next); x=(p^2*qr)%576; m[x+1]=x)); print(select(x->(x>408 && x<424), Set(m)))
[409, 413, 415, 419, 421]
-- 25.11.2022, 14:34 --The calculation time of the pattern with the same LCM will increase by 12 times. This is with a naive linear approximation. Rather, the growth will be
or so.
Для них можно ровно так же взять и ограничить простые, хоть до тех же 5e8. Это будет сильно дольше, но ведь всего один раз посчитать. И тогда интервал квадратичных переборов будет идентичен. А вся разница будет только из-за линейных переборов, которые должны давать примерно линейное время, т.е. всё же примерно в 12 раз, не 144.
. Полагаю, этот рекорд надолго.
.
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паттерна из 
основных. Количество таких паттернов возросло на 20 по сравнению с предыдущей таблицей. 
- 
- 
- 
- 
- 
- 
- 
- 
. This is not saying that 
is divisible by 3. For example 
.
after just over 44h of calculation. The last 4 hours took advantage of the additional mod 32 check, which made it about 30% faster. I plan to keep working to reduce that threshold for as long as calculations for 
in 2-3 days.
, but I'll probably put that to one side until we're closer to completing 
:
.
allocation has reached 
and 
before it starts to accelerate again. That's the speed on my computer, of course, but the slowest computer among the contributors is no worse than half as fast.
has the appropriate value 
? I can see that that could give some benefit. However I am, as always, nervous about how well debugged something with such a specific application would be. And if LCM=554400 patterns can already be completed in 48 hours (and improving) without this, the value is limited at least until we move on to 
). This is easy to estimate: the number of iterations of the linear search would be 
, a total of 180 for each prime number on the second level of recursion. And as the substituted prime increases (up to 1e8), the number of iterations will drop even further, down to 2.