3blue1brownWhy Long Primes Are Both Simple Yet Complex Looking Dividers
You might know what a prime number is, but have you ever heard the term "long prime"? If not, that's understandable. Long primes aren't that talked about because frankly, they don't seem to be all that useful. But when has that ever stopped mathematicians? Long primes actually have lots of interesting patterns and can lead us to pretty cool claims due to their restrictions. This video is an example of patterns we can decipher from such numbers and is mainly following\ my journey into discovering them and analysing them.
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Comments
7
It seems empty without music, but this video better than most I've seen
7
Clarity struggle a bit:
1) sometimes things implied, leading to incorrect statements like "square numbers are infinite"
2) in my opinion pronunciation is often not clear.
But overall I think video is good.
3.9
- I don't really see why should I care, nor do I see something special about the video.
- With the graphs of remainders, I'd like to see example for prime that is not long.
- 6:30-7:30 too complex, if the assumption is that the viewer is not familiar with the terms, I would introduce them in opposite order. I got quite lost after you expected me to remember multiple terms without knowing what they mean. Also wordy sentences like "modulo is related to function mod" are unnecessary.
- Video is too long. It contains ton's of stuff like explaining bases, lot's of python code etc.
3.4
I found this video to be reasonably clear overall, but really long and there was little to hold my attention. Now, full disclosure, I am not a mathematician. However, there were many other pure math videos that were able to hold my attention, so it is not the fact that I don't appreciate math. I guess my best advice for the author is to try to find ways of "mixing things up" a little, so that the video doesn't look and sound the same the whole time. Otherwise, it starts to sound monotonous.
5.5
Goal Orientation: 5/10
Novelty: 6/10
Thought-Provoking: 8/10
Comprehensibility: 4/10
Technological: 4/10
Overall Average: 5.4/10
3.8
I like learning about an exploration that reports on relations among several items. Perhaps some extra notation could simplify discussion and provide ways to clarify what matters.
Your animation of the middle-school algorithm for producing a decimal expression for N/D (a "reduced fraction") can be generalized as solving a sequence of equations for integer-valued variables (with 1 < B and 0 < R_i < D)
0. N = Q_0 * D + R_0
1. R_0 * B = Q_1 * D + R_1
2. R_1 * B = Q_2 * D + R_2
3. R_2 * B = Q_3 * D + R_3
4. etc
The Pigeonhole Principle guarantees the sequence {R_0, R_1, R_2, …} will eventually generate a duplicate value; the algebra implies both the R-sequence and the Q-sequence are repeating after that. The base-B expansion for N/D is Q_0 . Q_1 Q_2 Q_3 … and the finite set of R-values is a subgroup of Z-mod-D. In some cases, (B mod D) generates the full Z-mod-D group. (E.g., 3 is a primitive root mod 7 but 4 is not.).
4.9
A good basic video. Perhaps a bit long for the relatively simple material. I feel you belabour the point in a few places, however one person's 'over-explained' is another's 'clear and complete'. Still, I'd suggest this video would have been better if it was edited back to around 25 minutes.
Sound is a bit inconsistent - a little bit echoey at some points, fine at others. I assume you recorded in more than one session.
But those are both only minor grumbles.
7.1
Interesting.