# Calculating an algorithm from a set of pre generated numbers

Hi, I have 10 different 16-digit  codes that were  all generated with a single  unknown  algorithm and  I was wondering if there is some sort of program or something that I can enter  the 10 codes into and  the program will be able to study the data and create an algorithm that fits with the data I fed it? The goal of finding the algorithm is so I can generate two more codes (I have 10 but I need 12)

Below is the 10 codes that I have (they were all originally made using an unknown algorithm)
9812040200460433
9812040200999308
9812040202831088
9812040204719773
9812040207085554
9812040208584216
9812040209296057
9812040209807048
9812040231599584
9812040238072516

Any idea on how to do this, or if it can even  be done?
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Commented:
After the 98120402 there could just be a random 8 extra digits. Are there more criteria that these codes need to comply with? Perhaps a checksum calculation? There isn't much to go on with just that group of numbers.
Commented:
There are an infinite number of algorithms that could have generated those 10 numbers.
Without some way of judging which of them might be more likely to be your unknown algorithm,
there would be no reason to think that any other numbers generated by those algorithms would have any relation to what your unknown algorithm does.

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Commented:
>>  There are an infinite number of algorithms . . .

And if you want to entertain yourself for hours:

1.  Try looking at the differences between successive numbers.
Maybe a pattern will emerge.
Did they come in that order, or did you sort them?

2.  Look at the list in terms of modular arithmetic.
Maybe all the numbers equal 193 mod 439   and   107 mod 541.
Commented:
An important additional bit of information would be "Did you list the numbers in the order that they were generated?"

If you did there is a way of generating two additional unique numbers from the ones listed.
Graph the last eight digits. Fit the graph with a 9th degree polynomial. Extrapolate that equation to the next two numbers.
There are several variations on this procedure which you can try (une non linear graphing)
The probability that this procedure will give you two more useful numbers depends on what you want to do with the numbers. If you just want two unique numbers, this will work. If you want to do something with the numbers the probability of useful numbers is very small.
Author Commented:
thanks for the info!
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