Somehow, when you factor a number, if you write the factors of

What about 8

8 = 2•2•2

But 222 isn't prime

>>7970060
10 -> 2 * 5 -> 25

Sorry, bud.

>>7970060
2342356
factorized: 2*2*97*6037
22976037/9=2552893
faggot

>>7970070
fuck me, what are you thinking!? 10? is this a joke?

OP: interesting. what does it mean?

>>7970068
you dont get it
8->2*2*2->222->2*3*37->2337->3*19*41->31941->.........->3331113965338635107

>>7970070
you also dont get it
25->5*5->55->5*11->511->7*73->773

So you keep doing it and eventually get a prime?

>>7970077
>2342356
you have to do it repeatedly:

2342356->2*2*97*6037->22976037->3*3*7*364699->7*373*129209->7373129209

>>7970093
You always get a prime dude

I have the proof here but its to long to fit in this post

I think
59389280910761603526921019
doesn't end in a prime number.

>>7970102
This is pretty interesting.

Does this result have a name

>>7970096
You mean you factorize until you can't factorize anymore and then it's prime? genius!

>>7970060
You're just continuously repeating a process until you get a prime number.

Did you know that if you add one to a number, you get a prime? Proof:

2: 2 + 1 = 3
12: 12 + 1 = 13
14: 14 + 1 = 15 --> 15 + 1 = 16 --> 16 + 1 = 17

Amazing, isn't it?

>>7970113
I dont know I just came up with it

>>7970082
That’s actually interesting. How about giving this a name and circlejerking on it?

>>7970124
Lets call it the /sci/ conjecture

>>7970124
Are you legit retarded?

>>7970117

>>7970129
No one is adding +1 to anything faggot

File: 1409168093125.png (116KB, 480x480px) Image search: [Google]

116KB, 480x480px

>>7970060
whoa it's almost like if square a number and subtract 1 you get a prime number every time.

>>7970060
You have a proof that no infinite chains can occur?

>>7970060
https://oeis.org/A037274

>>7970140
Also I think that it's uninteresting to only consider base 10.

>>7970164
Good find, and the sequence apparently can include -1 where "no prime is ever reached."

>>7970181
Technically it can but none has been found so far. The chance of finding one is zero.

>>7970186
>The chance of finding one is small.
Fixed

What if you were to see how many repetitions were necessary for each number to become prime to see if a pattern were to form

>>7970210
No, the chance of finding one is literally zero. Do you understand how probability works?

>>7970270
you dont know what youre talking about

>>7970135
>what is 15

>>7970060
cool story bro

https://www.youtube.com/watch?v=kxuU8jYkA1k

>>7970278
Wow, Dunning Kruger in effect ladies and gentleman. The basic idea is that the sum of the chances of each iteration of the sequence being prime diverges even as the iterations get larger and the chance of them being prime decreases. I would outline it more accurately but you would probably not understand it. Idiot.

>>7970324
not him, but please do, i would like to know more

>>7970060
Somehow, if you take any number and I mean ANY number and add 1 to it will increase in quantity. Few examples:

1+1 = 2
4573+1 = 4574
-2+1 = 3

>>7970263
I have made it to number 20 starting from 2 .the number of repetitions necessary are as follows with 0 representing a number that is already prime.
0,0,2,0,1,0,1,4,2,4,0,1,0,5,4,4,0,1,0,6
with the frequency of number of repetitions being
8 zeros
3 ones
2 twos
0 threes
4 fours
1 five
1 six

>>7970082
This is amazing if it holds in general.

Can someone write a program to determine if it holds for all numbers up to, say, 100 or 1000?

>>7970347
OK, let's say for simplicity's sake that each iteration adds about p digits to the number where p is the number of prime factors. The number of prime factors of a number n is approximately log log n. The number of digits of n is approximately log n. So a number with k digits will have approximately log k prime factors and this means that the next iteration of this number will have k + log k digits.

k
k+logk
k+logk+log(k+logk)
...
F(t) = k+tlog(kt) as t dominates

The chance of a number with k digits being prime is approximately 1/k, so the chance of the iterations containing a prime is sum from t=0 to inf of 1/F(t), which diverges

>>7970060
So the factors [math]p_1\cdot p_2\cdot...[/math] can be used as the [math]a[/math] terms in the series [math]\sum\limits_{i=1}^{k}a_{i}10^{k-i}[/math] where [math]k[/math] is the number of p's? This reminds me of how when you add the digits of multiples of 9, you get 9. This is p. interesting anon.

>>7970380
No. That is not what is being said. Try again.

>>7970393
Well, I left out the part about factorizing the series again and again until you reach a prime.

http://mathworld.wolfram.com/HomePrime.html

>>7970397
No, you forgot that prime factors can have more than one digit.

>>7970402
ayy lmao thanks senpai. didn't see that.

Can someone make an applet that lets you enter numbers and display the chains resulting?

>>7970406
See >>7970164

>>7970400
Nice.

Seems there's no known proof that it always converges to a prime, though probabilistically it will.

>>7970400
Mystery solved

>>7970377
>sum from t=0 to inf of 1/F(t), which diverges
Assuming you mean infinum with "inf", this makes zero sense

The infinum of 1/F(t) should be a number (not infinity), how is a sum with finite elements supposed to diverge?

>>7970102
Cool story Fermat. Proof or gtfo

>>7970425
I mean infinity.

>>7970117
>>7970351
>>7970119
Retards. That it always becomes a prime at some point is literally an unsolved problem.

https://en.m.wikipedia.org/wiki/Home_prime

>>7970435
Either way, if a probability diverges, you have made some serious mathematical error, probabilities can never be less than 0 or more than 1

>>7970445
>pick a number
>do some arbitrary shit
>something happens
somehow the fact that it's not proven yet makes the problem less dull and retarded?

>>7970520
It's an approximation, if you haven't noticed. The point is, the numbers don't grow large enough fast enough to not have a prime. This is a heuristic argument, not a proof.

>>7970284
He means Mersenne primes. Basically you just define some way to find primes and check if its prime. If it is, you call it a "Your name here" prime.

OP, you should sent Brady Haran an email.

>>7970640
>OP, you should sent Brady Haran an email.
Done

>>7970060
>1
>only factor is 1
>no self respecting mathematician considers 1 a prime number

>>7970921
stupid idiot

Just because it's unsolved doesn't mean it's cool. It just means fuck those stupidly large numbers that would be their upper bound

>>7970102
>I have the proof here but its to long to fit in this post
epin

>>7970351
>-2+1 = 3

>>7970978
> stupid ad hominemt

>>7970540
No its that OP is obviously a liar and doesn't have a proof

>>7970102
nice memes fermat

>>7970406

>can somebody casually make an applet that is able to efficiently perform prime factorization?

Sure, bub. Just let me finish cracking these RSA keys, and I'll get started.

>>7971870
>He called me out on being stupid and posting idiotic things, what do I do? Oh! I'll pretend we're having an argument and call for fallacies HEHEHE

fuck off, stupid idiot

>>7970082
So if you have a number X and you write down its factors that makes a number. Repeat the step if that number is not prime.
TADAAH! after N steps, the number is suddenly prime!
Why would this be? Maybe because you're discarding the result if it's not prime.
Your example is analogous to the following:
Pick a random number,
if it's not prime: pick a random number
the result is prime
omgsosmart.jpeg

>>7970445
>https://en.m.wikipedia.org/wiki/Home_prime
I actually read your link, and the problem is if HP(49) = HP(77). It's not the question why this happens, because that is ridiculously obvious.
Good source by the way, too bad it doesn't support your cause.

>>7972258
this, you >>7970082 have no way of determining how many steps its going to take for your algorithm to return a prime number. maybe it has use in generating psuedorandom numbers?

>>7972262
>I actually read your link, and the problem is if HP(49) = HP(77).
How is it a problem?

>>7972279
because it required you to calculate the prime factors of a 220 digit number or something. That's a problem, not "hurr durr, why does this algorithm always give me a prime number?".

>>7971929
I fail to see the part that's stupid. The part that's a well accepted fact or the past where I used said well accepted fact to disprove OP's hypothesis. Not only have you failed to counter my argument, you've also managed to unnecessarily make a complete ass of yourself not once but twice.
>inb4 hurr durr you're still a stupid idiot