I am going to post an answer that is maybe not helpful for the exact goals, but which will maybe help restate the problem to be easier. As commenters noted it is super big and complex, many whole careers have been devoted to solving very small parts of this problem.
Possible problems with premise
I think that this question starts from this statement as a ...
A spin column might work for your purposes since you can do multiple rounds of binding if your volume is too large to bind in a single pass, but for DNA of that size a lot will be irreversibly stuck to the column. See for example the protocol for the Monarch® PCR & DNA Cleanup Kit.
Consequently I would recommend just doing an ethanol precipitation, ...
In addition to the answer by Maximilian Press, the papers
 Intrastrand Parity Rules of DNA Base Composition and Usage Biases of
 Properties of a General Model of DNA Evolution Under
show that under a no-strand-bias assumption, the base frequencies of a single strand at equilibrium, denoted as $A^*,T^*,G^*,C^...
I have tested a similar design to this. With a duplex protocol the chance of forming a hairpin is much higher than that of forming self-dimer, even at concentration of 25 μM. You can run a 3-5% agarose gel to test the outcome.
DNA is a large molecule which is particular interest relies in the succession of nucleotide that composes it. The genetic information is contained in the succession of nucleotides (I will ignore epigenetics here for simplicity). A given position of any length on the DNA molecule is called a locus.
A gene is typically defined as a protein coding sequence. ...