Prime and Multiple Numbers Count

Postby daniel » Mon Nov 10, 2008 7:29 am

[quote=Joe]
Daniel, how can i include 1 as a prime number as 1 is not prime number,?,
[/quote]

Hi Joe,
Why is the prime number filter setting required for those two draws not the same as the actual number of prime numbers?
daniel
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Postby Jerzy » Mon Nov 10, 2008 9:16 am

Daniel and Joe,

Some mathematicians regard number 1 as a prime number and some mathematicians think that it is not prime number. I do not know who is right and who is not.

Even if we accept that 1 is the prime number, it is better not to include this number in the filter. Inclusion of 1 into prime numbers filter can decrease the performance of the filter, because there will be too many numbers in the group, 16 instead of 15. I recommend to leave the prime number filter as it is now.

Number 1 can be addressed more than enough using filters for other special numbers. Number 1 is very common in these special numbers groups.
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Postby Jerzy » Mon Nov 10, 2008 10:01 am

Joe,

I imagine that the filtering of special numbers can be best done in the Special Numbers Filter. Because the list of special numbers is long, 2 or 3 Special Numbers Filters might be necessary.

Happy Numbers and Lucky Numbers have nice names.

It is difficult for me to explain number theory issues on the Forum, and it is also not necessary. The information on special numbers is available on the Internet, particularly at mathworld.wolfram.com and wikipaedia. Use Google search.

Just to give you an idea on Happy Numbers I will show you how to check that number 7 is a happy number:

You square the digit of 7
7^2=49
and square the digits in 49 and add them
4^2+9^2=16+81=97
and square the digits in 97 and add them
9^2+7^2=81+49=130
and square the digits in 130 and add them
1^2+3^2+0^2=10
you do the same for 10
1^2+0^2=1
you come down to 1 which means that 7 is the happy number.

How Lucky Numbers are generated? A kind of sieve is used.

From the string of consecutive numbers remove every second number (all evens) then remove every 3rd number from the remaining numbers, then every 7th number from the remaining numbers. Continue this process. The numbers which survive this process are the lucky numbers.

Mathematical properties of these special numbers are probably not much relevant if we include them in lotto filters. But it is important that they have stiff, inflexible patterns, cannot be regarded as random combinations of numbers, and usually appear only at limited number of positions in a ticket.
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Postby Jerzy » Mon Nov 10, 2008 11:21 am

Hi everyone,

In one of my latest posts I included a list of Special Numbers groups in the range applicable for 49 number lottery.

This list can be expanded if we "wheel" each group of numbers.

I will show you how to do it for Hexagonal Numbers, but it can be done for any number group.

Hexagonal Numbers:
01, 06, 15, 28, 45
02, 07, 16, 29, 46
03, 08, 17, 30, 47
04, 09, 18, 31, 48
05, 10, 19, 32, 49
06, 11, 20, 33, 01
07, 12, 21, 34, 02
08, 13, 22, 35, 03
09, 14, 23, 36, 04
10, 15, 24, 37, 05
11, 16, 25, 38, 06
12, 17, 26, 39, 07
13, 18, 27, 40, 08
14, 19, 28, 41, 09
15, 20, 29, 42, 10
16, 21, 30, 43, 11
17, 22, 31, 44, 12
18, 23, 32, 45, 13
19, 24, 33, 46, 14
20, 25, 34, 47, 15
21, 26, 35, 48, 16
22, 27, 36, 49, 17
23, 28, 37, 01, 18
24, 29, 38, 02, 19
25, 30, 39, 03, 20
26, 31, 40, 04, 21
27, 32, 41, 05, 22
28, 33, 42, 06, 23
29, 34, 43, 07, 24
30, 35, 44, 08, 25
31, 36, 45, 09, 26
32, 37, 46, 10, 27
33, 38, 47, 11, 28
34, 39, 48, 12, 29
35, 40, 49, 13, 30
36, 41, 01, 14, 31
37, 42, 02, 15, 32
38, 43, 03, 16, 33
39, 44, 04, 17, 34
40, 45, 05, 18, 35
41, 46, 06, 19, 36
42, 47, 07, 20, 37
43, 48, 08, 21, 38
44, 49, 09, 22, 39
45, 01, 10, 23, 40
46, 02, 11, 24, 41
47, 03, 12, 25, 42
48, 04, 13, 26, 43
49, 05, 14, 27, 44

If you continue the lines will repeat.

The numbers in each next line increase by 1, and when the highest number used in the lottery is reached, it becomes 1 in the next line.
This way we create 49 groups of numbers which can be used as filters.

We can enter these groups of numbers into Match Numbers Filter, and build a re-useable compact filter. The filter setting for each group of numbers need not be the same or should not be the same.

Use Back-test function of the Match Number filter to see how a group of numbers performed in the past.

Building such compact filter requires a lot of work, but the filter is re-useable.

If the numbers in lines increase by 1 compared with the previous line, it restores the balance of odd and even numbers in the process of filtering e.g.:

02, 03, 05, 07, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 (the majority are the odd numbers)
03, 04, 06, 08, 12, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48 (the majority are the even numbers)

The most important point is that we can multiply possible number group filters by "wheeling" number groups.

Good Luck!
Jerzy
 
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Postby daniel » Tue Nov 11, 2008 1:08 am

[quote=Joe]
Daniel, how can i include 1 as a prime number as 1 is not prime number,?,
[/quote]

Hi Joe,
I do not communicate very clearly. If you include the the number 1 as a prime number, then the setting for the prime number filter agrees with the number of prime numbers found in the 6 numbers of the drawing.
Is this what you find?
daniel
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Postby Joe » Wed Nov 12, 2008 5:44 am

Daniel, sorry for the mis-understood your statements, Now i will do what you want me to do here, Do you want me to include this number as prime number?,
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Postby Joe » Wed Nov 12, 2008 5:47 am

jezry, nicely explained, I already thought of doing something like this filter, let me have time to think what I can do on this idea, thanks, mean time enjoy my new "match Number distance" filter, thanks
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Postby daniel » Wed Nov 12, 2008 2:12 pm

[quote=Joe]
Daniel, sorry for the mis-understood your statements, Now i will do what you want me to do here, Do you want me to include this number as prime number?,
[/quote]

That's OK Joe,
Just leave it as it is.
Thanks again for your help, and the new plugins.
daniel
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Postby Jerzy » Wed Nov 12, 2008 2:46 pm

Thank you Joe! Your latest filters are enjoyable and very useful.
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Postby CSenior » Thu Nov 13, 2008 1:53 am

Joe~ Well done on the latest filters! Thank you! Kudos!
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Postby teoman » Mon Nov 17, 2008 9:35 pm

[quote=Joe:1226197059]
[quote=kookoo]any information on how to apply this filter?[/quote] its simply counting the Prime numbers and multiples. for example for the combination 7,21,23,27,48,49,

we can count the Prime and multiples of numbers, like

Prime numbers are 7, 23, (2 numbers)
and multiples of 3 are 21,27,48 (3 numbers)
and multiples of 4 is 48 (1 number)
and multiples of 6 is 48, (1 number)
multiples of 7 are 7,21,49 (3 numbers),
multiples of 8 is 48 (1 number),
and multiples of 9 is 27 (1 number),[/quote]
Hi Joe,

Your filter Prime and Multiple Numbers Count is very useful, I think it is possible to simplify further by reducing from 8 settings, how many are now, at 5 settings, because some numbers are repeated from one group to another by 2, 3 to 4 times.

Arrangement of numbers after the current settings

Prime numbers => 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, (15 numbers)
Numbers multiples of 3 => 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, (16 numbers)
Numbers multiples of 4 => 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, (12 numbers)
Numbers multiples of 5 => 5, 10, 15, 20, 25, 30, 35, 40, 45, (9 numbers)
Numbers multiples of 6 => 6, 12, 18, 24, 30, 36, 42, 48, (8 numbers)
Numbers multiples of 7 => 7, 14, 21, 28, 35, 42, 49, (7 numbers)
Numbers multiples of 8 => 8, 16, 24, 32, 40.48, (6 numbers)
Numbers multiples of 9 => 9, 18, 27, 35, 45, (5 numbers)

Unused => 1, 22, 26, 34, 38, 46, (6 numbers)

Arrangement of numbers after eliminating those who repeat

Prime numbers => 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, (15 numbers)
Numbers multiples of 3 => 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, (15 numbers)
Numbers multiples of 4 => 4, 8, 16, 20, 28, 32, 40, 44, (8 numbers)
Numbers multiples of 5 => 10, 25, 35, (3 numbers)
Numbers multiples of 7 => 14, 49, (2 numbers)

Unused => 1, 22, 26, 34, 38, 46, (6 numbers)

If it was possible it would mean to have a few options to configure the settings.
The most common include:

2 3 1 0 0
3 2 1 0 0
3 3 0 0 0
2 4 0 0 0
4 2 0 0 0

Good Luck!
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Postby Joe » Tue Nov 18, 2008 4:08 am

ok tem, but I think its nice to have more options rather than reducing the options, before i make this change, i would like have suggestions from others too who are using this filter, thanks
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Postby Jerzy » Tue Nov 18, 2008 5:53 am

teoman and Joe,

The Prime Numbers and Multiples filters in its current form works as a set of 8 number group filters. They work independently from each other and the resulting outcome is the sum of their filtering power.

If we remove some numbers from the groups it will decrease the filtering power of the filter, particularly if we decrease the number groups we want to filter. And if the multiples of 7 are limited to 14 and 49, this group will be applicable only to the games with 49 numbers, (it will be useless for other games).

The total tickets removed using the filter proposed by teoman would be smaller than that achieved by using the original Joe's filter (using comparable settings, because you cannot use the same settings). Additional filtering with "unused" numbers group will not compensate for this loss.

Try experimenting with the Joe's filter and compare its results with the results achieved with the Match Numbers filter using the groups suggested by teoman.

Reducing the filtering power of this filter offers no advantage. I am quite happy with the current form of this filter. Of course it can be improved by including more number groups to filter. It would increase its filtering power.
Jerzy
 
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Postby Joe » Tue Nov 18, 2008 6:01 am

[quote=Jerzy]Reducing the filtering power of this filter offers no advantage. I am quite happy with the current form of this filter. Of course it can be improved by including more number groups to filter. It would increase its filtering power.[/quote]Exactly jerzy,
Teoman~ if you dont want to use those options you can simply dont select those options, thats why I gave in count options, I try to include unused numbers as teoman's wish, thanks
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Postby CSenior » Tue Nov 18, 2008 6:13 am

[quote=Jerzy]
... I am quite happy with the current form of this filter. Of course it can be improved by including more number groups to filter. It would increase its filtering power.
[/quote]

Jerzy~ Well said!

Joe~ I agree with Jerzy's post. Would it be possible to add more number groups to the filter?

Thanks!
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