mersenneforum.org  

Go Back   mersenneforum.org > Great Internet Mersenne Prime Search > Math

Reply
 
Thread Tools
Old 2006-02-13, 17:18   #34
R. Gerbicz
 
R. Gerbicz's Avatar
 
"Robert Gerbicz"
Oct 2005
Hungary

101101110102 Posts
Default

Quote:
Originally Posted by Citrix
cool. May be this will solve the problem for 88.
Yes, maybe. Do you know that these numbers are Snfs targets? However it's Snfs difficulty is 1024 bits, larger than the current world record...
R. Gerbicz is offline   Reply With Quote
Old 2006-02-13, 21:41   #35
Citrix
 
Citrix's Avatar
 
Jun 2003

1,579 Posts
Default

I don't know about snfs, never used it.

I have a related question. Can 2^n-x (for x small, say x<100) be n smooth. especially when x=1?

Any solutions for this one? (Other than the first few trivial cases)

Citrix
Citrix is offline   Reply With Quote
Old 2006-02-13, 21:59   #36
grandpascorpion
 
grandpascorpion's Avatar
 
Jan 2005
Transdniestr

503 Posts
Default

I doubt if there's any solutions to it. There's no low solutions right? Unless you count n=1
grandpascorpion is offline   Reply With Quote
Old 2006-02-13, 22:23   #37
grandpascorpion
 
grandpascorpion's Avatar
 
Jan 2005
Transdniestr

503 Posts
Default

Sorry, I was looking only at x=1
grandpascorpion is offline   Reply With Quote
Old 2006-02-13, 22:26   #38
Numbers
 
Numbers's Avatar
 
Jun 2005
Near Beetlegeuse

22·97 Posts
Default

If a is the first term in the sequence, then \large \frac{2^{n}-x}{n}= integer when \large x\,=\,a+nt,\,t=(0,\,10),\,x<100.

But I only checked for n is prime.

Last fiddled with by Numbers on 2006-02-13 at 22:31
Numbers is offline   Reply With Quote
Old 2006-02-13, 22:30   #39
grandpascorpion
 
grandpascorpion's Avatar
 
Jan 2005
Transdniestr

1111101112 Posts
Default

Hi Numbers, would do you mean exactly by "a" being the first term in the sequence?
grandpascorpion is offline   Reply With Quote
Old 2006-02-13, 22:38   #40
Numbers
 
Numbers's Avatar
 
Jun 2005
Near Beetlegeuse

1100001002 Posts
Default

Let \large n\,=\,7, then \large \frac{2^{7}-x}{7}= integer when \large x\,=\,2,\,9,\,16 etc.

So 2 is the first term in the sequence and each subsequent term is 2+(7t) where t =(0, 10).
Numbers is offline   Reply With Quote
Old 2006-02-13, 22:42   #41
grandpascorpion
 
grandpascorpion's Avatar
 
Jan 2005
Transdniestr

7678 Posts
Default

Gotcha, thanks
grandpascorpion is offline   Reply With Quote
Old 2006-02-13, 22:48   #42
Citrix
 
Citrix's Avatar
 
Jun 2003

1,579 Posts
Default

Quote:
Originally Posted by Numbers
Let \large n\,=\,7, then \large \frac{2^{7}-x}{7}= integer when \large x\,=\,2,\,9,\,16 etc.

So 2 is the first term in the sequence and each subsequent term is 2+(7t) where t =(0, 10).

Numbers, n smooth does not mean it has to be divisible by n. (even if it does I meant, that all the prime factors are less than or equal to n)

Citrix

edit: you can also rule out all prime n since 2^p-1 has factors of the forum 2*k*p+1 which is >p. For that matter all 2^n-1 can also be ruled out, even 2^n-2^k such that 2^k<100.

Then the lowest case under consideration is 2^n-3. Example 2^2-3 is 2 smooth, 2^7-3 is 5 smooth and so on.
I would also like the question for the 2^n+x side? (2^3+1 is 3 smooth)

Last fiddled with by Citrix on 2006-02-13 at 23:00
Citrix is offline   Reply With Quote
Old 2006-02-13, 22:54   #43
Numbers
 
Numbers's Avatar
 
Jun 2005
Near Beetlegeuse

22×97 Posts
Default

Quote:
Originally Posted by Citrix
I meant that all the prime factors are less than or equal to n.
Actually, I should have said that t = (0, 1, 2, ...), then it would be a proper sequence.

My sequence identifies those cases (or some of them, at least) where there might be a solution. It was never intended to be a complete solution on its own. The next step is to determine those numbers in my sequence that are divisible by prime < n.

Edit.
In fact, on thinking about it, I realise that I have not excluded the possibility that these numbers are not divisible by some p > n, so it is in fact completely useless.

Why is it that whenever I try to help you, all I do is confuse the issue :-)

Last fiddled with by Numbers on 2006-02-13 at 23:07
Numbers is offline   Reply With Quote
Old 2006-02-13, 23:40   #44
wblipp
 
wblipp's Avatar
 
"William"
May 2003
New Haven

3×787 Posts
Default

Quote:
Originally Posted by Citrix
Can 2^n-x (for x small, say x<100) be n smooth.
28-81 is 8 smooth
wblipp is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Fermat number and Modulo for searching divisors CyD Factoring 4 2011-05-31 11:24
Odds that a Random Prime is a Number? R.D. Silverman Homework Help 60 2010-10-13 10:31
Odds that a random number is prime Number theory Homework Help 4 2009-08-28 22:04
Odds of a prime number being random Orgasmic Troll Lounge 6 2007-08-11 04:09
Number of divisors of n? Citrix Math 10 2006-02-08 04:09

All times are UTC. The time now is 07:55.

Sat May 8 07:55:48 UTC 2021 up 30 days, 2:36, 0 users, load averages: 6.08, 5.14, 4.55

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.