Comments by "Le YASEP" (@leyasep5919) on "Is 1 a Prime Number?" video.

Now I understand ! 1 is a prime number IF we work in the additive/Goldbach domain. It is not in the multiplicative domain because 1 is the neutral element of multiplication (which is most used because Goldbach's conjecture is not yet proved)
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That's a really important question and the response is yes 😛 I love seeing mathematicians arguing 😛
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@angelmendez-rivera351 I love when convictions meet reality. "Is 1 a prime number" is a matter of opinion and this video gives the best arguments for both. Yes if you work in the additive/Goldbach domain, no if you're in the multiplicative domain. No teacher will bother explaining that.
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@angelmendez-rivera351 * "peer-reviewed sources" are a relatively recent practice. * I'll have to rewatch the video but it introduces a lot of historical context. * Goldbach's conjecture is a link between the additive and multiplicative structures.
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@angelmendez-rivera351 I've looked at the subject for "a while" now and so far the only conclusion I could draw is "the primality of 1 is a convention". You stick to a particular rule and definition so you are not wrong and that's fine, it works for you.
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@angelmendez-rivera351 Give me some slack please, I just published a little blurb about Galois and just fnished 2 other articles, I need some me time to start the next.
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@angelmendez-rivera351 I am strange. Maybe even a crackpot 😛 Anyway, the video here presents a lot of perspectives that I agree with. I hope he'll go further and deeper because he's a great teacher. Anyway here is a real question : consider an algorithm that, given a prime number, generates the next prime number. This algorithm is one in the well known family of wheel algorithms. The smallest integer that can "bootstrap" the algorithm is 1. Does that imply that 1 is a prime ? If 1 is not a prime, then how come it creates another prime ?
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@angelmendez-rivera351 You state that "if such an algorithm did exist, the fact that prime inputs produce prime outputs does not imply composite inputs cannot produce prime outputs. " However by construction, the algorithm is proven to necessarily generate composite output when fed composite input. Otherwise, it would imply that Eratostene's sieve (from which wheels are derived) does not work.
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@angelmendez-rivera351 I hope my answer with all the links has not been censored by youtube... if you need more, contact me personally by email.
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@angelmendez-rivera351 I can't find the long message I wrote here, it was even erased for me. contact me by email, so I can send you more links, and even working code to show that your reading was incomplete.
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@angelmendez-rivera351 "A sieve is not a prime-generating algorithm." well, what are they for then ? 😀 There are factorisation versions but they can only do that if they somehow generate primes. I have a few old references to Pritchard's works and others, more recent. I feel dumb for having written so much along with links, now I'll have to rewrite it...
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@angelmendez-rivera351 "you are sorely mistaken about how all sieves work in general. " I'm not speaking about ALL sieves. There are other types of sieves used in advanced number theory that I don't deal with at all.
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@angelmendez-rivera351 "You have already made it clear that you are unable of changing your mind," Nor will you. I try to address your concerns and furthermore : my mind doesn't matter, nor does yours because maths and algorithms are not emotions or opinions. I prove with code that an assertion is true, an algorithm creates the result that is embedded in its structure. We can interpret but "changing my mind" will not make the algorithm work or fail. So from construction, and not opinion, there are processes that give certain results. I may be "completely in the wrong about how sieves work." but then how do you explain these results ? I'm not Grothendieck, I may even be a crackpot. But either the result is right, or not, and that's all that matters.
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@angelmendez-rivera351 "the fact that you have to rely on links, rather formal source citation," => I can strip the URL from the DOI refs but it felt nicer to provide the text as well. Now you might have seen that wheel sieves are used for certain kinds of factorisation. You seem to have stopped there. It does not have to be limited to this application though. Here is the output of a sample wheel code that was initialised with 1: New prime: 2 Primorial: 2 New size: 1 New wheel: [2] New prime: 3 Primorial: 6 New size: 2 New wheel: [4, 2] New prime: 5 Primorial: 30 New size: 8 New wheel: [6, 4, 2, 4, 2, 4, 6, 2] New prime: 7 Primorial: 210 New size: 48 New wheel: [10, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, 2, 4, 8, 6, 4, 6, 2, 4, 6, 2, 6, 6, 4, 2, 4, 6, 2, 6, 4, 2, 4, 2, 10, 2] Tell me how it didn't generate a sequence of prime numbers. Tell me how the fact that you think I don't understand this mechanism makes this somehow impossible. The result is there : the wheel sieve can be configured to generate a new prime from the previous (and a previous wheel) and the algorithm was primed with a single 1.
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