mersenneforum.org A Sierpinski/Riesel-like problem
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2016-12-29, 18:02   #56
sweety439

Nov 2016

2,819 Posts

Quote:
 Originally Posted by sweety439 The (probable) primes with n > 1000 for the completed-started extended Sierpinski/Riesel problems (with bases b <= 24, except R2, R3 and R6) are: S4: 186*4^10458+1 S7: (141*7^1044+1)/2 S10: 804*10^5470+1 S12: 404*12^714558+1 378*12^2388+1 S16: (23*16^1074+1)/3 S17: 10*17^1356+1 S18: 122*18^292318+1 381*18^24108+1 291*18^2415+1 R4: (106*4^4553-1)/3 74*4^1276-1 296*4^1275-1 ( = 74*4^1276-1, the two primes are the same, since 296 = 74 * 4) R7: (367*7^15118-1)/6 (313*7^5907-1)/6 (159*7^4896-1)/2 (429*7^3815-1)/2 (419*7^1052-1)/2 R12: (298*12^1676-1)/11 R17: (29*17^4904-1)/4 (13*17^1123-1)/4
A prime is missing for R17: 44*17^6488-1.

Thus, the list of R17 should be:

44*17^6488-1
(29*17^4904-1)/4
(13*17^1123-1)/4

2016-12-29, 18:28   #57
sweety439

Nov 2016

2,819 Posts

Quote:
 Originally Posted by Batalov Staying away from words that have an established meaning in the community is probably a good idea before you actually can talk the language of the community. How do you know that you are not actually meaning 'weak' when you are saying 'strong'? Or rather, how do you know that things you are talking about are altogether related? Because they aren't! If one proved Goldbach, the would have also proven weak Goldbach. If one proved weak Goldbach (and they did!), then nothing happened to Goldbach. If you (well, let's imagine) proved "The strong Sierpinski problem", then ... ... Nothing would happen to the "normal" Sierpinski problem, of course! Origin: https://xkcd.com/1310/
For example, in the most popular Riesel base 10 case, the smallest original Riesel number base 10 is conjectured to be 10176, but the smallest strong Riesel number is proven to be 334, since all numbers of the form (334*10^n-1)/gcd(334-1,10-1) are divisible by 3, 7, 13 or 37, all numbers of this form are composite. However, if we research all k's < 10176 (except the k's that are proven composite, these k's are 334, 343, 1585, 1882, 3340, 3430, 3664, 7327, 8425, 9208, k=343 and 3430 are proven composite by partial algebraic factors, other k's are proven composite by covering set), then the problem covers the original Riesel base 10 problem. This problem (the strong Riesel base 10 problem) has only 3 k's < 10176 remain: 2452, 4421 and 5428. (see the links https://www.rose-hulman.edu/~rickert/Compositeseq/ and http://www.worldofnumbers.com/Append...s%20to%20n.txt)

The top primes of this problem are: (with k < 10176, n > 10000)

7019 (881309)
8579 (373260)
6665 (60248)
1935 (51836)
1803 (45882)
1231 (37398)
6373 (37156)
1343 (29711)
6742 (22850)
505 (18470)
3499 (12689)
3356 (13323)
450 (11958)

The test limits for the remain k's < 10176:

2452 (554K) (see https://www.rose-hulman.edu/~rickert...siteseq/#b10d3)
4421 (1.69M) (see http://www.noprimeleftbehind.net/cru...onjectures.htm)
5428 (300K) (see http://www.worldofnumbers.com/Append...s%20to%20n.txt)

Last fiddled with by sweety439 on 2016-12-29 at 18:53

 2016-12-29, 19:18 #58 pepi37     Dec 2011 After milion nines:) 24·89 Posts You copy for other resources very well
 2017-01-01, 18:31 #59 sweety439   Nov 2016 2,819 Posts In fact, I am interested in finding (probable) primes of the form (a*b^n+c)/gcd(a+c,b-1), with integers a, b, c, a > 0, b > 1, c != 0, gcd(a,c)=1, gcd(b,c)=1. Also see http://mersenneforum.org/showthread.php?t=21819 for the generalized minimal primes search for some triples (a, b, c) without known (probable) primes. Last fiddled with by sweety439 on 2017-01-01 at 18:37
 2017-01-01, 19:08 #60 sweety439   Nov 2016 B0316 Posts The old file is wrong for R6, the smallest extended Riesel number to base 6 should be 84687, not 84686. Update correct text file. Attached Files Last fiddled with by sweety439 on 2017-01-01 at 19:09
2017-01-01, 20:17   #61
pepi37

Dec 2011
After milion nines:)

24·89 Posts

Quote:
 Originally Posted by sweety439 In fact, I am interested in finding (probable) primes of the form (a*b^n+c)/gcd(a+c,b-1), with integers a, b, c, a > 0, b > 1, c != 0, gcd(a,c)=1, gcd(b,c)=1. Also see http://mersenneforum.org/showthread.php?t=21819 for the generalized minimal primes search for some triples (a, b, c) without known (probable) primes.

In fact : you are very well in copying other stuff.

2017-01-02, 03:07   #62
gd_barnes

May 2007
Kansas; USA

288416 Posts

Quote:
 Originally Posted by pepi37 In fact : you are very well in copying other stuff.
He is quite amazing at doing that isn't he?

Or is it she? Sweety, are you female?

What is your native language? I (we) kind of feel like you don't quite understand our posts sometimes.

 2017-01-02, 09:48 #63 pepi37     Dec 2011 After milion nines:) 24·89 Posts Maybe she / he will understaned ban?
2017-01-02, 13:35   #64
sweety439

Nov 2016

2,819 Posts

Quote:
 Originally Posted by gd_barnes He is quite amazing at doing that isn't he? Or is it she? Sweety, are you female? What is your native language? I (we) kind of feel like you don't quite understand our posts sometimes.
Oh, I know, you means I should not post my own research here?

No, I am not female.

Last fiddled with by sweety439 on 2017-01-02 at 14:13

2017-01-02, 14:02   #65
pepi37

Dec 2011
After milion nines:)

26208 Posts

Quote:
 Originally Posted by sweety439 Oh, I know, you means I should not post my own research here?
You dont have your "own research" you have only copies from others.
And yes, you should not post "your" irrelevant research here...

2017-01-02, 14:11   #66
sweety439

Nov 2016

281910 Posts

Quote:
 Originally Posted by pepi37 You dont have your "own research" you have only copies from others. And yes, you should not post "your" irrelevant research here...
I really download those programs, but my computer cannot run them. (my computer is windows 10)

However, I have some programs, and found some (probable) primes, such as (29*17^4904-1)/4.

The extended Sierpinski/Riesel problems are really my own research, and I proved the extended Riesel base 17 problem.

Last fiddled with by sweety439 on 2017-01-02 at 14:13

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