/sci/ - Science & Math

>>15085642
it's just another way of stating the fact that besides 2 and 3, all primes are congruent to 1 or -1 mod 6

>>15085642
C'mon, man, I know you're the one who posted the similar question for "factor of 6" and "6k +/- 1" recently: >>15076218
Surely you can apply what you learned in that thread.

>>15085642
>there are no irrational prime numbers

>>15085669
all irrationals are prime

>>15085642
fucking kek i see what you did

>>15085642
False. 3 is neither a factor of 30 nor 30k +- j

>>15085712
>>15085675
Retards...

>>15085712
what are the factors of 30?

>>15085738
1,2,5,6,15,30

>>15085712
this guy

>>15085740
what is 3x10?

>>15085712
brainlet

>>15085746
3 and 10 are not in the list that i replied with

>>15085642
is this a new /sci/ meme ?

>>15085757
what is 3x10?

>>15085778
irrelevant

>>15086048
3x10 = 30, thus 3 and 10 are factors of 30

>>15085642
>this thread again
>this time modulo 30

>>15086071
bro my mind is fucking blown!!

>>15086114
holy shit

guys this is getting to be too much for me I only learnt the other day that all primes are either a factor of 2 or 1 off from a multiple of 2

>>15085642
7 is not a factor of 30 ,how what ,is it pysop to destroy my basic mathematics

>>15086198
it gets worse
>>15086205
why would 7 have to be a factor of 30?

>>15085642
Ok, let's say you have a number of the form 30k+5 (for nonnegative k). Why is this either a factor of 30 or not prime? If k is 0, then it's just 5. Otherwise, since 30k is a multiple of 5 (5 is a factor of 30), 30k+5 is also a multiple of 5, so it's not prime. This list, ±{1, 7, 11, 13}, is just what you get when you eliminate everything that has any factor of 30 as a factor. That happen to be quite a lot. If it seems weird to you that so many number are eliminated, just think of how the prime numbers get more and more sparse as they get larger, and think of how in the sieve of Eratosthenes entire algebraic sequences are removed.

>>15086205
The fact that 7 is coprime with 30 is precisely why 30k+7 for k > 0 is not NECESSARILY composite.

>>15086307
i acc didnt know that

>>15085675
But if pi is prime then pi squared is the product of two primes. Primality is a number theoretic notion. I think the best way to think of it is as the minimal generating set of the monoid of natural numbers under multiplication. The primes have to be in any generating set, because you can't generate any prime form other elements, and this necessary set is in fact sufficient, because everything is only excluded because it can be generated by primes. 1 is considered to be able to be generated by primes because it's the identity element, it's a 0-ary product.

>>15086114
I peer reviewed and accept this

>>15086205
>>15086305
Think about the numbers in a cycle of 30, such that n = 30k + j, j < 30

>Any evens above 2 are obviously even, so they're not prime.
That leaves 1, 2, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29
>30k + 9, 15, 21, 27 are divisible by 3, so not prime
That leaves 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 25, 29
>30k + 25 is divisible by 5, so not prime
That leaves 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
>2, 3, and 5 are factors of 30, so they are covered by clause 1
That leaves 1, 7, 11, 13, 17, 19, 23, 29
>{17, 19, 23, 29} is the same as 30 - {13, 11, 7, 1}, so we can make that a plus/minus
That leaves 1, 7, 11, 13 for clause 2

>>15085642
All primes are of the form [math]2k+n,k \in \, \mathbb{N} \in {0,1} [/math]

>>15086370
All primes are of the form n, [math] n \in \mathbb{N} [/math]

>>15086327
>But if pi is prime then pi squared is the product of two primes
So?

>>15086405
pi squared is also irrational, and so we have arrived at a contradiction of the fact that no prime is the produce of other primes. It cannot be the case that "all irrationals are prime".

>>15086338
Good explanation.

>>15086423
by that logic 3 isn't a prime either because it's the product of the square root of 3 with itself. in fact there are no primes.
so prime numbers are allowed to have nontrivial irrational factors, and so there is no problem with saying that all irrationals are prime. dumbass

>>15086431
3 being a prime doesn't make sqrt(3) a prime. I was simply proving that it cannot be the case that "all irrationals are prime" by contradiction. Primes are by definition natural numbers, so it is a ridiculous thing to consider to begin with, but I was just showing how it wouldn't make sense even if we forget that primes aren't BY DEFINITION naturals.

>>15086423
pi squared isn't prime because it's the square of pi

>>15085642
now do 210

>>15086438
>3 being a prime doesn't make sqrt(3) a prime
No, but sqrt(3) is irrational and thus prime, so 3 is a prime number that's a product of other prime numbers. Hence irrationals can be prime even with irrational factors

>>15086445
Only natural numbers can be prime you fuckwit.

>>15085675
now let's concern ourselves with the topic of 0(zero) being prime

You guys actually believe in prime numbers? You really think 3 isn't divisible by anything but 1 or itself? Then what do you get when you multiply 5 by 0.6?

>>15086451
but what if .... could I use my master BS debating skills then?

No primes are a factor of 30.

>>15086444
[math]\text{All primes are either:}\\
1)\ \text{A factor of 210.}\\
2)\ 210k \pm j, k \in \mathbb{N}, j \in \{1, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103\}[/math]

>>15085740
I thought he meant multiple

>>15086464
[math]
\frac{30}{2} = 15 \checkmark\\
\frac{30}{3} = 10 \checkmark\\
\frac{30}{5} = 6 \checkmark\\
[/math]

Holy shit, how?

>>15086484
Bedeviled sorceress, oddity of sin, retreat from my humble chambers and bugger men no more. Thine form beguiles and amuses the weak of will and heart and mind while tempting the amateur of body and appetite. I shant stand a moment sooner then to smite my soul with the perverse and wicked. Your vulgarity consumes my humble nature and returns but a fiery spirit; rage descendeth upon you. Rage that I carry for all man such that they may temper their blades and impale you - as you so beg. Would sheathing a thousand quench your thirst or would it take a thousand more. Come now, let us discuss no further for science is an empirical art bringing knowledge upon the most faithful observer.

>>15086066
fuck you

>>15086114
amazing result !

>>15086638
wait til you see >>15086270

>>15086484
wtf

>>15086270
include me in legendary screencap

>>15085712
thats bullshit but i believe it

>>15086270
Posts like this are literally the only reason I still come here

Thank you anon

>>15086645
>>15086647
>>15086643
So many worthless trash over her on this board discussing prime numbers on a high school level and making memes as if they are some clevel intellectual geniuses like the midwits who laugh at stupid people thinking they are really clever and what not.

What a bunch of worthless children do your homework!

>>15086688
>t. redit pseud

Have a (tip)

>>15086690
Do your homework worthless trash, you're even worse than redditors making fun of idiots while yourself being a midwit, do YOUR HOMEWORK CHILD

>>15086691

>>15086691
>>15086688
This thread is for serious mathematical discussions. Please keep your "trolls" in /b/ where they belong.

>>15086752
>510510
Good, but I believe you can do better

>>15086773
I can. Unfortunately I can't post it here, due to image limits

>>15086776
Your dedication is commendable regardless, anon.

>>15086752
god i love this board

>>15086752
did you do this by hand?

>>15086205
7 is -13 modulo 30

>>15085654
It's another way of stating that primes above 30 are congruent to ± 1,7,11,13 mod 30

>>15086819
Put your dick away, anon

>>15087365
you mean 17 right?

can someone explain why this works?

>>15085642
>All primes are not multiples of 2 or 3
Groundbreaking

>>15089215
this dummy really forgot that 2 is a factor of 2 and 3 is a factor of 3

People keep posting these but nobody ever mentions how it's useful to cryptography.

>>15085642
I thought it was all a factor of 6 because 1+2 is the same as 3+3?

>>15090867
1+2 = 3
1+2+1+2 = 6
1+2+1 = 5
1+2+1+2+1=7
1+2+1+2+1+2=9
1+2+1+2+1+2+1+1=11?

>>15090867
>1+2 is the same as 3+3
??

>>15086773

>>15086773
>>15086776
>>15086777
>>15086819
>>15087354
Here you go.

>>15086270
WOW

>>15090957
Holy shit. Why does this work?

>>15090957
Rare and based anon.

>>15090957
WHAT THE FUCK

>>15090957
brainlet here, how does this work?

>>15090957
STOP YOU'RE MESSING WITH THE NATURAL ORDER

>>15086752
>>15090957
[math]\text{First 10 primes: } \{2, 3, 5, 7, 11, 13, 17, 19, 23, 29 \}\\
\\
1)\ 2 = 2\\
2)\ 2 \cdot 3 = 6\\
3)\ 2 \cdot 3 \cdot 5 = 30\\
4)\ 2 \cdot 3 \cdot 5 \cdot 7 = 210\\
5)\ 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 = 2310\\
6)\ 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \cdot 13 = 30030\\
7)\ 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \cdot 13 \cdot 17 = 510510\\
8)\ 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \cdot 13 \cdot 17 \cdot 19 = 9699690\\
9)\ 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \cdot 13 \cdot 17 \cdot 19 \cdot 23 = 223092870\\
10)\ 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \cdot 13 \cdot 17 \cdot 19 \cdot 23 \cdot 29 = 6469693230[/math]

Why does a pattern emerge for numbers 6-8 and then break after that?

>>15085642
I have the old factoring app i wrote on my old phone still
it's the modified prime sieve alg? [proper name??]

>>15094376
> pick x primes
> field is prod(x)
> coprimes are primes not in x, plus their products that fall within field
> pick number y
> y mod field == coprime is gcd(y, field)=1

>>15092359

Let these type of symmetric numbers be 'nice' numbers. Some examples: [math]1212, 30030, 510510, 9699690[/math]. Notice that you can always factorize these numbers to the form [math]p\cdot10^q\cdot(10^r+1)[/math], where p is not a multiple of 10:
[math]\begin{align} 1212=12\cdot10^{2}+12&=12\left(10^{2}+1\right) \\ 510510&=51\cdot 10^1\left(10^{3}+1\right)\\ 9699690&=969\cdot10^1\left(10^{3}+1\right)\end{align}[/math]

Now what sets these 'nice' numbers apart from any number that can written in this form is that in their case [math]p[/math] should be [math]\leq r[/math]. Just try to fiddle with a calc to see why this is the case: why say

[math]\begin{align} 931\left(10^{3}+1\right) &= 931931 \ \ (p = 3\leq r ) \\ 3100\left(10^{3}+1\right) &= 3103100 \ \ (p = 2 \leq r)\end{align}[/math]

are nice numbers but [math]9312\left(10^{3}+1\right) = 9321312[/math] ( note: [math]p=4\nleq r[/math]) didn't turn out to be so nice

Also in your list of numbers only the prime factorials of 6,7,8 satisfies this condition. And shouldn't be hard to prove that they are the only ones that are 'nice'

>>15092359
Let these type of symmetric numbers be 'nice' numbers. Some examples: [math] 1212, 30030, 510510, 9699690 [/math]. Notice that you can always factorize these numbers to the form [math] p\cdot10^q\cdot(10^r+1) [/math] , where p is not a multiple of 10:

[math] \begin{align} 1212=12\cdot10^{2}+12&=12\left(10^{2}+1\right) \\ 510510&=51\cdot 10^1\left(10^{3}+1\right)\\ 9699690&=969\cdot10^1\left(10^{3}+1\right)\end{align} [/math]

Now what sets these 'nice' numbers apart from any number that can written in this form is that in their case [math] p [/math] should be [math] \leq r [/math]. Just try to fiddle with a calc to see why this is the case: why say

[math] \begin{align} 931\left(10^{3}+1\right) = 931931 \ \ (p = 3\leq r ) \\ 3100\left(10^{3}+1\right) = 3103100 \ \ (p = 2 \leq r)\end{align} [/math]

are nice numbers but [math] 9312\left(10^{3}+1\right) = 9321312 [/math] ( where [math] p=4\nleq r [/math]) didn't turn out to be so nice

Also in the list of numbers only the prime factorials of 6,7,8 satisfies this condition.

>>15094680
also pic

>>15090957
LOL

>>15094376
the original is Sieve of Eratosthenes
Sieve of Pritchard is similar?
it's a modified prime sieve alg, probably just a no-name one

>>15096205
>>15094376
scans up to 7,500,000 for primes in 13-17 sec on the old 1ghz single core

>>15096247
probably not any decent sieve then. My computer can do it in less than a second. Even though it's 4ghz, it shouldn't be 13-17x faster.