mersenneforum.org if p is prime, factors of 2^p-1? - Is it possible?
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2020-10-23, 09:12   #23
LaurV
Romulan Interpreter

Jun 2011
Thailand

2·7·653 Posts

Quote:
 Originally Posted by ONeil A composite number produced from a prime number using 2^p-1 does contain prime factors!
What is that?

How do you "produce a composite number from a prime number"? Do you multiply it with 7? Or subtract 53? Can you prove that, by doing so, you don't end with another number which is still prime?

And you want to do that by "using 2^p-1". How? You take 2^p-1 and hit your prime number in the head with it until it becomes composite?

And what the hack is "contains prime factors" having to do with the way you "produced" it? All composite numbers contain prime factors, regardless of how you "produced" them. All prime numbers "contain prime factors" too (themselves).

Man, how old are you? You may be like 12 years old or so, learning the basics right now, and not having the proper way to express yourself in English yet, and in that case, you may be a genius and become great in the future. At that age I didn't have any idea about all this stuff. If that's the case, my apologies.

But if you are older than 18, stop the funking trolling and go learn the lingo, if you want to talk math.

P.S. I never pretended to be a decent person.

Last fiddled with by LaurV on 2020-10-23 at 09:40

 2020-10-23, 09:40 #24 Viliam Furik   "Viliam FurÃ­k" Jul 2018 Martin, Slovakia 14816 Posts I would love a way to give a "like" or some kind of positive evaluation of my opinion to the post, without having to write another one, saying I like it. Hmmm, Xyzzy ? Last fiddled with by Viliam Furik on 2020-10-23 at 09:41
2020-10-23, 11:56   #25
Dr Sardonicus

Feb 2017
Nowhere

23×181 Posts

Quote:
Originally Posted by Viliam Furik
Quote:
 Originally Posted by a1call Meant 2^p-1 If for any prime p 2*p+1 | 2^p-1 Then 2*p+1 is definitely prime. The test is deterministic and computationally about as expensive as a PRP test.
This works with only k=1, thus if it divides 2p-1, it is definitely a prime factor.
Actually, it's true for more than just k = 1.

Let p > 2 be prime. The smallest conceivable composite factor of 2p - 1 is (2p+1)2.

So if q = 2*k*p + 1 divides 2p - 1, and k < 2*p + 2, then q is prime.

Alas, it is more than likely that if k < 2*p + 2 and q = 2*k*p + 1 is prime, that q does not divide 2p - 1.

Especially if q is congruent to 3 or 5 (mod 8)

2020-10-23, 12:00   #26
LaurV
Romulan Interpreter

Jun 2011
Thailand

914210 Posts

Quote:
 Originally Posted by Dr Sardonicus So if q = 2*k*p + 1 divides 2p - 1, and k < 2*p + 2, then q is prime.
Respective k<6*p+1 when p=1 (mod 4)

2020-10-23, 12:28   #27
Dr Sardonicus

Feb 2017
Nowhere

23·181 Posts

Quote:
Originally Posted by LaurV
Quote:
 Originally Posted by Dr Sardonicus So if q = 2*k*p + 1 divides 2p - 1, and k < 2*p + 2, then q is prime.
Respective k<6*p+1 when p=1 (mod 4)

2020-10-25, 05:35   #28
ONeil

Dec 2017

24×3×5 Posts

Quote:
 Originally Posted by LaurV What is that? How do you "produce a composite number from a prime number"? Do you multiply it with 7? Or subtract 53? Can you prove that, by doing so, you don't end with another number which is still prime? And you want to do that by "using 2^p-1". How? You take 2^p-1 and hit your prime number in the head with it until it becomes composite? And what the hack is "contains prime factors" having to do with the way you "produced" it? All composite numbers contain prime factors, regardless of how you "produced" them. All prime numbers "contain prime factors" too (themselves). Man, how old are you? You may be like 12 years old or so, learning the basics right now, and not having the proper way to express yourself in English yet, and in that case, you may be a genius and become great in the future. At that age I didn't have any idea about all this stuff. If that's the case, my apologies. But if you are older than 18, stop the funking trolling and go learn the lingo, if you want to talk math. P.S. I never pretended to be a decent person.
Your comprehension is weak go back to school and take a math class.

2020-10-25, 19:53   #29
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

2×3×1,543 Posts
A red card given

Quote:
 Originally Posted by ONeil Your comprehension is weak go back to school and take a math class.
Mod note: please refrain from rude remarks.
A warning ban from forum communication is applied, 2 days. next level is 7 days, then a month.

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