20200712, 18:35  #892 
Nov 2016
9A1_{16} Posts 

20200712, 18:42  #893  
Nov 2016
5×17×29 Posts 
Quote:
R88 k=400: since 400 is square, all even n have algebra factors, and we only want to know whether it has a covering set of primes for all odd n, if so, then this k makes a full covering set with algebraic factors and be excluded from the conjecture; if not, then this k does not make a full covering set with algebraic factors and be included from the conjecture. nvalue : factors 1 : 3 · 3911 3 : 7 · 101 · 128519 5 : 13 · 12119 · 4466239 7 : 3^3 · 3799333 · 53118563 9 : 7 · 167 · 36096764394509957 11 : 13 · 25136498347515268468841 13 : 3 · 1877 · 1156907 · 5976181 · 64998862429 15 : 7^2 · 239 · 6079 · 483551 · 1173283 · 485185295929 17 : 13 · 7417 · 1573883316708285469700513209073 and there is covering set {3, 7, 13} (n == 1 mod 6: factor of 3; n == 3 mod 6: factor of 7; n == 5 mod 6: factor of 13), thus for R88, k=400 proven composite by partial algebra factors. R10 k=343: since 343 is cube, all n divisible by 3 have algebra factors, and we only want to know whether it has a covering set of primes for all n not divisible by 3, if so, then this k makes a full covering set with algebraic factors and be excluded from the conjecture; if not, then this k does not make a full covering set with algebraic factors and be included from the conjecture. nvalue : factors 1 : 3 · 127 2 : 37 · 103 4 : 3 · 127037 5 : 17 · 37 · 73 · 83 7 : 3^2 · 42345679 8 : 37 · 113 · 613 · 1487 10 : 3 · 2399 · 52954163 11 : 37 · 103003003003 and there is covering set {3, 37} (n == 1 mod 3: factor of 3; n == 2 mod 3: factor of 37), thus for R10, k=343 proven composite by partial algebra factors. Last fiddled with by sweety439 on 20200712 at 19:13 

20200712, 18:49  #894 
Nov 2016
5×17×29 Posts 
For Sierpinski side:
Case gcd(k+1,b1) = 1 is the same as the Sierpinski side of CRUS Case k = 1, b even is the same as finding the smallest generalized Fermat prime base b Case k = 1, b odd is the same as finding the smallest half generalized Fermat prime base b Case k = b2 is the same as finding the smallest prime of the form ((b2)*b^n+1)/(b1) For Riesel side: Case gcd(k1,b1) = 1 is the same as the Riesel side of CRUS Case k = 1 is the same as finding the smallest generalized repunit prime base b Case k = b1 is the same as finding the smallest Williams prime base b (primes of the form (b1)*b^n1, some authors use base (b1) instead of base b for (b1)*b^n1, but I don't think this is good, since the "base" should be the number with an exponent) 
20200712, 18:50  #895  
Nov 2016
5×17×29 Posts 
Quote:
Thus, if n is large, a probable prime (k*b^n+1)/gcd(k+1,b1) can be proven to be prime if and only if gcd(k+1,b1) = 1. 

20200712, 18:54  #896  
Nov 2016
5×17×29 Posts 
Quote:


20200712, 18:55  #897  
"Sam"
Nov 2016
2·3·53 Posts 
Quote:
Also, have you considered where n^2+n+1, n^2n+1, n^2+1, are partially factored? I could keep going you know. Last fiddled with by carpetpool on 20200712 at 19:05 

20200712, 19:14  #898  
Nov 2016
5·17·29 Posts 
Quote:


20200712, 19:16  #899  
Nov 2016
5·17·29 Posts 
Quote:
(not consider the case that b is square, since any square k for any square Riesel base b proven composite by full algebra factors) Last fiddled with by sweety439 on 20200712 at 19:18 

20200712, 19:47  #900 
Nov 2016
5×17×29 Posts 
These bases b have many small Sierpinski/Riesel numbers k:
Code:
base Sierpinski numbers k Riesel numbers k 5 == 7, 11 mod 24 == 13, 17 mod 24 8 == 47, 79, 83, 181 mod 195 == 14, 112, 116, 148 mod 195 9 == 31, 39 mod 80 == 41, 49 mod 80 11 == 5, 7 mod 12 == 5, 7 mod 12 12 == 521, 597, 1143, 1509 mod 1885 == 376, 742, 1288, 1364 mod 1885 13 == 15, 27 mod 56 == 29, 41 mod 56 14 == 4, 11 mod 15 == 4, 11 mod 15 16 == 38, 194, 524, 608, 647, 719 mod 819 == 100, 172, 211, 295, 625, 781 mod 819 17 == 31, 47 mod 96 == 49, 65 mod 96 18 == 398, 512, 571, 989 mod 1235 == 246, 664, 723, 837 mod 1235 19 == 9, 11 mod 20 == 9, 11 mod 20 20 == 8, 13 mod 21 == 8, 13 mod 21 21 == 23, 43 mod 88 == 45, 65 mod 88 23 == 5, 7 mod 12 == 5, 7 mod 12 25 == 79, 103 mod 208 == 105, 129 mod 208 27 == 13, 15 mod 28 == 13, 15 mod 28 29 == 4, 11 mod 15 or == 7, 11 mod 24 or == 19, 31 mod 40 == 4, 11 mod 15 or == 13, 17 mod 24 or == 9, 21 mod 40 32 == 10, 23 mod 33 == 10, 23 mod 33 Last fiddled with by sweety439 on 20200712 at 19:50 
20200712, 20:26  #901  
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
2×3×7×211 Posts 
There are several reasons not to quote an entire post:
1. It causes the reader to have to scroll past the giant block to get to fresh content.   If someone is trying to catch up on a thread it slows them down. 2. It does not help the reader know particularly what bit of the quote that is being referred to. 3. If it is the immediately preceding post, a quote is not needed at all. 4. If someone is searching the forum to find something, excessive quoting produces extra hits that are chaff and not wheat. 5. It slows forum operation and adds extra unneeded volume to the database. An example of an effective quote: Quote:
Dog 6 Dog 7 Notice that the limited quote tells the user what is being referred to. The concept of Hypertext was that things could be referenced without placing an entire work in the document. This is done all of the time in documents, a small bit is quoted and there are footnotes to the original work. Last fiddled with by Uncwilly on 20200712 at 20:27 

20200714, 11:51  #902 
Nov 2016
5×17×29 Posts 
Found an error of S81: (34*81^734+1)/gcd(34+1,811) is prime
Double checking S81.... 
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