The bigger the primorial you use
The bigger the primorial you use, the fewer are the divisors
that you will
end up producing and checking. You can generalize this approach by
creating a table with primorials and another table with the coprimes of
each primorial (should take about a minute for the following code to
run):
-- create and populate table primorials
if object_id('dbo.primorials') is not null
drop table dbo.primorials;
go
create table dbo.primorials
(
p
bigint not
null constraint
pk_primorials primary
key,
primorial bigint
not null constraint unq_primorial
unique
);
insert into dbo.primorials(p, primorial) values(2, 2);
insert into dbo.primorials(p, primorial) values(3, 6);
insert into dbo.primorials(p, primorial) values(5, 30);
insert into dbo.primorials(p, primorial) values(7, 210);
insert into dbo.primorials(p, primorial) values(11, 2310);
insert into dbo.primorials(p, primorial) values(13, 30030);
insert into dbo.primorials(p, primorial) values(17, 510510);
insert into dbo.primorials(p, primorial) values(19, 9699690);
go
-- create and populate table coprimes
-- should take about a minute
if object_id('dbo.coprimes') is not null
drop table dbo.coprimes;
go
create table dbo.coprimes
(
primorial bigint
not null,
coprime
bigint not
null,
constraint
pk_coprimes primary key(primorial, coprime)
);
declare @primorial as
bigint;
declare cursor_primorials
cursor
fast_forward for
select
primorial from dbo.primorials
order by
primorial;
open cursor_primorials;
fetch next from cursor_primorials into
@primorial;
while @@fetch_status
= 0
begin
insert into dbo.coprimes(primorial, coprime)
select
@primorial, n from
dbo.fn_nums(1, @primorial)
where not exists(select * from dbo.primorials
where
primorial <= @primorial and n % p = 0);
fetch next from
cursor_primorials into @primorial;
end
close cursor_primorials;
deallocate cursor_primorials;
go
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