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I imagine this could be used as a universal Identifier.

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I guess it depends on the particular stretch of DNA. Some sections of DNA are conserved and under heavy selection pressure (such as p53) whereas others can vary. –  Bez Aug 21 at 18:05

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Here is what the data says. UK government must have had some scientific evidence when it settled on a 10 variable-length sections of genome for their database, SGM+. In one such variable sections, some people have 10 repeats of CTTT, others have 11, others have 12 etc. The largest of those fragments, at its maximum length, are about 350 base pairs. The US government uses 13 such variable-length sequences for its CIA database, called CODIS. On both sides of the Atlantic, roughly 3-4 thousand base pairs were judged to be enough, with some safety margin, by the most advanced geneticists in the world, working on public money.

The catch is that these variable length sequences are disjoint, so you end up requiring far more than 4,000 bp. If you need these markers on the same DNA strand (chromosome), you should space them by 50 centimorgans, at which distance they recombine independently. But according to http://www.sciencemag.org/site/feature/data/genomes/265-5181-2094.pdf , the longest chromosome only has 350-400 centimorgan. It means you cannot get 10 independent DNA sequences on a human chromosome, be it the longest.

I predict there is no such continuous DNA stretch, that would tell apart any two non-twins. Since it is much better to use multiple chromosomes in DNA fingerprinting, I doubt you will find more relevant experimental data.

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When designing PCR primers we typically use a minimum length of 20 bases, because the probability of a sequence of N bases appearing by random is $\frac{1}{4^N}$, and $\frac{1}{4^{20}}$ is about 9x$10^{-13}$, or about 1 in a trillion. Since the human genome is a little over 3 billion bases long, a 20 base sequence should appear only once. However, most of an individual's DNA isn't random, it's inherited from their parents, and they got their's from their parents, etc. Long story short, there isn't a lot of unique DNA in any given person. The uniqueness is only visible on the large scale, you have half of your DNA from your father, and half from your mother. So would any of your siblings, but the specific DNA they got from each parent would be different from yours.

I think we can calculate the odds of getting a specific set of chromosomes from a parent. If there are 23 pairs of chromosomes, then the probability of getting any given set should be $\frac{1}{2^{23}}$, since we have 2 parents, the odds of getting your specific set of DNA is $(\frac{1}{2^{23}})^2$, which is about 1 in 70 trillion. So the odds of you having a non-identical twin that has the same DNA as you is very low. But any given 20 base sequence should have a 50% probability of appearing in you and the sibling.

But if we look at 2 20 base sequences of DNA in you and your sibling, and each had a 50% chance of appearing, then the probability of both sequences appearing in the both of you is 25%. If we add a third, it goes to 12.5%, and so on. If there are 7 billion humans on earth, we need a probability of less than 1 in 7 billion, and $2^{33}$ is about 8.6 billion, so if you looked at 33 different sites on the genome it should be able to differentiate you from every human on the planet

By the way, did I do the math right? I'm not a mathmagician and I could have made a mistake in my probability calculations. I have also assumed that the spontaneous mutation rate and crossing over rates are low enough to ignore, but both would serve to make your DNA a little more unique.

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