Prime factor exponent notation is a way to express a number as a product of its prime factors, where each prime factor is raised to an exponent that indicates how many times that factor is used in the product. This notation is particularly useful in number theory for simplifying calculations, finding factors, and understanding the properties of numbers.

This is an extremely widely used technique as of 2020 and much earlier.

If allows you to amplify "any" sequence of choice (TODO length limitations) between a start and end sequences of interest which you synthesize.

If the sequence of interest is present, it gets amplified exponentially, and you end up with a bunch of DNA at the end.

You can then measure the DNA concentration based on simple light refraction methods to see if there is a lot of DNA or not in the post-processed sample.

Even Ciro Santilli had some contact with it at: Section "How to use an Oxford Nanopore MinION to extract DNA from river water and determine which bacteria live in it", see: PCR!

One common problem that happens with PCR if you don't design your primers right is: en.wikipedia.org/wiki/Primer_dimer

Sometime it fails: www.reddit.com/r/molecularbiology/comments/1kouomw/when_your_pcr_fails_again_and_you_start/and a comment:

In 2020 physics, best explained by general relativity.

TODO: does old Newtonian gravity give different force results than general relativity?

As you would expect, not much secret here, we just dumped a 1 liter glass bottle with a rope attached around the neck in a few different locations of the river, and pulled it out with the rope.

And, in the name of science, we even wore gloves to not contaminate the samples!

The first thing we had to do with the sample was to extract the DNA present in the water in a pure form for the PCR.

We did that with a Qiagen DNeasy PowerWater Kit.

As you would expect, this consists of a purification procedure with several steps.

In each step we take a physical or chemical action on the sample, which splits it into two parts: the one with the DNA and the one without.

We then take the part with the DNA, and throw away the one without the DNA.

The first steps are coarser, and finer and finer splits are done as we move forward.

One cool thing we did in this procedure was to use magnetic separation with magnetic beads to further concentrate the DNA: Figure 1. "GE MagRack 6 pipetting.".

The beads are coated to stick to the DNA, which allows us to easily extract the DNA from the rest of the solution. This is cool, but bio people are borderline obsessed by those beads! Go figure!

Then we prepared the DNA for sequencing with the Oxford Nanopore specific part: Oxford Nanopore SQK-LSK109 Ligation Sequencing Kit.

Here some of the steps required a bit more of vortexing for mixing the reagents, and for this we used the VELP Scientifica WIZARD IR Infrared Vortex Mixer which appears to be quicker to use and not as strong as the Vortex Genie 2 previously used to break up the cells:

After all that was done, the DNA of the several 400 ml water bottles and hours of hard purification labour were contained in one single Eppendorf!

www.fishersci.no/shop/products/nalgene-polysulfone-reusable-bottle%20-top-filters/10465781 (archive)

This is where we poured the water. It was not large enough for the entire 1L sample, so we had to do it a few times.

www.gelifesciences.com/en/us/shop/protein-analysis/protein-sample-preparation/protein-enrichment/magrack-6-p-05761 (archive).

The third one from Cambridge after:

Rational representation can refer to different concepts depending on the context, but it is most commonly associated with mathematics, particularly in number theory and algebra. 1. **In the context of numbers**: A rational representation usually refers to the expression of a number as a ratio of two integers.

Replaces Thymine in RNA.