Thank you so much,,,  to all of you !!!

What seemed to me a good way (open c.dat for binary);
I found out to be not good,
when the records stored in this file they become 1 billion, GET e PUT it slows down a lot,
...probably because this method does not use much RAM.

I repeat;
The number I want stored for compare are in the range 0  to 33bit.
No all number in the range the program create, only approximately 20 -30 %.
The program create these number billion of time.
Every when a program create an number I have to know if that number is already processed, then store how many times.
thats is all,
no other.

I think the solutions OPEN c.dat for binary is for the moment the best I try.
If you have other solution muck speed write to me.

The numbers generated by the array   q1   q2  .... q31    they can be  stored together in an singe  registry,
but in some way they must be associated with  howmanytimesalreadyprocessed (range 1 - 255 )

the registry  it must not have  references  of  the  number  has arrived by q1 or q2...

the strategies I tried are the following:

strategy1;
create file.txt  for any number that the program create
into this .txt file write howmanytimesthisnumberalreadyprocessed
To do this I do;
 - IF _FILEEXISTS  (if 0 is an new number , if -1 no new number)
 - OPEN FOR APPEND  (if no exist this procedure create the file)
 - WRITE  1  (append new line in .txt file contain "1"   -  it can also be good in this way)
 - CLOSE

strategy2;
DIM Array(1 to 8589934590) AS _UNSIGNED _BYTE
 - IF Array(mynuber) = 0  THEN  GOTO ......
 - IF Array(mynuber) = >0  THEN  Array(mynuber)  =  Array(mynuber)  +1

strategy3;
OPEN "c.dat" FOR BINARY AS #1
GET #1  ,   mynumber  ,   howmanytimesthisnumberalreadyprocessed

 - IF   howmanytimesthisnumberalreadyprocessed  >  0  THEN     PUT #1  ,  mynumber  ,  howmanytimesthisnumberalreadyprocessed  + 1 :GOTO...

 - PUT #1  ,  mynumber  ,  1

If you know only 20% will be different AND they are relatively random, 1.6 billion 20% of 8 billion. if it's 32-bit values, makes a shade over 6 billion bytes. Really, with a bit of squeezing in a b-tree, you might be able to squeeze that out quickly. TreeSort and use no disk for the sort. Also a HashTable can do the job. or even CountingSort. I'd recommend HashTable as the fastest way for random sets. Even ordered sets, but then why would you ask? But I digress. HashTables provide a fast, convenient way to search for things and correctly constructed, yield an average access of 1.25 seeks/find (or not) and very nearly  0(1) insertion. That too is another doable approach. If you cannot spare space for that and have a brick-wall limit of 6GB, you can run this in segments and mege the results. You could use SteveSort or HashListSort. Both will be pretty quick. HashListSort will even give you a sorted result too.

I,m sorry,,,
I did not understand anything,,,,not a word,,,

my question;
in the program I'm making, I estimated that the processing process is 2 years.
I have to adopt more strategies to get the maximum speed.

In some phases of the program, I have numbers in the range (1 to 8.589.934.591) (33bit)
NOT all numbers in the range, ONLY 20%.

I have to check if the number I'm processing has already been processed and how many times.

thank you all,
now I'm testing your suggestions,
then I will let you know which ones are most suitable for my needs.