18 November 2005

   This evening home is snowing, so nice, I miss the snow and flakes... I was just thinking about prime numbers and why people had such a fascination about them. In mysticism every number has a powerful meaning, a power coming from inside, and therewith attracts certain powers from exterior, is strange, hard to understand all this, especially how all numbers can be reduced to a number between 1 and 9.    Every philosophy has a little truth in it.
   I was trying to find a nice article on number reduction, for example the one from sourceryforge could be useful. Last week I implemented a function which returns the reduction of any sequence, could be date or number. I was intending to apply it on prime numbers, but even if can be observed certain similarities between different chains, is difficult to believe this will lead anywhere. CREATE FUNCTION dbo.NumberReduction( @text varchar(50)) RETURNS smallint /* Purpose: reduces to number a sequence of digits Parameters: @text varchar(50) - digits sequence Notes: the function works with any sequnce of alphanumeric, not numeric values being ignored Sample: SELECT dbo.NumberReduction('11/17/2005') SELECT dbo.NumberReduction('1234') SELECT dbo.NumberReduction('1234 8993 90003 3456') */ BEGIN    DECLARE @index smallint    DECLARE @total int    SET @index = 1    SET @total = 0    --for each char in alphanumeric sequence    WHILE (@index<=len(@text))    BEGIN          IF IsNumeric(Substring(@text, @index, 1)) = 1          SET @total = @total + Cast(Substring(@text, @index, 1) as smallint)       SET @index = @index+1    END    --if the number is not in 1..9 range, it calls further the NumberReduction for the new total    IF len(@total)>1       SET @total = dbo.NumberReduction(@total)    RETURN @total END Now, returning to prime numbers, I tried to generate the prime numbers between 1 and 1000000 and analize how many prime numbers are for each thousand. SELECT PrimeNumber/1000 DataSet , count(*) NumberPrimeNumbers FROM PrimeNUmbers GROUP BY PrimeNumber/1000 ORDER BY DataSet As it seems the maximum number of prime numbers is reached for the first thousand and decreases. DataSet*1000 Number Prime Numbers -------------------- ------------------ 0 (2..1000) 168 1 (1001..2000) 135 2 (2001..3000) 127 3 ........... 120 4 ........... 119 5 ........... 114 6 ........... 117 7 ........... 107 8 ........... 110 9 ........... 112 10 .......... 106 11 .......... 103 12 .......... 109 13 .......... 105 14 .......... 102 15 .......... 108 16 .......... 98 17 .......... 104 18 .......... 94 19 .......... 104 20 .......... 98 ........................... 980 ......... 67 981 ......... 75 982 ......... 70 983 ......... 70 984 ......... 70 985 ......... 76 986 ......... 76 987 ......... 63 988 ......... 71 989 ......... 72 990 ......... 71 991 ......... 79 992 ......... 65 993 ......... 68 994 ......... 78 995 ......... 69 996 ......... 69 997 ......... 83 998 ......... 74 999 ......... 65 That's all for today, is hard to believe somebody will read this :) today, anyway a nice weekend to everybody!

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