A Sierpinski/Riesel-like problem - Page 19

sweety439 · 2017-05-05, 12:59

Quote:

Originally Posted by kar_bon

(1654*30^38869-1)/29 is 3-PRP!
(1654*30^38869-1)/29 is Lucas PRP!

A few hours work done and tested with pfgw64.

How about a page of your results instead of doc's or txt-files without any explanation in it?

Thanks very much!!!
There are some 1k, 2k or 3k bases which you can sieve: (please do not sieve the GFNs and half GFNs, since only n=2^m where m>=0 can be prime)

Code:

base  remain k      n testing limit
S10   269           24K
S25   71            10K
S33   67, 203, 407  6K
S36   1814          6K
R7    197           29K
R33   257, 339      6K
R43   13            6K
R61   37, 53, 100   5K

sweety439 · 2017-05-05, 13:15

Update the text files for the most recent status.

sweety439 · 2017-05-05, 13:21

Corrected the text files: Should list ",NA" instead of ",0". (the errors are in the text files for SR42 and SR60)

sweety439 · 2017-05-05, 13:25

Now, all extended Sierpinski/Riesel bases b<=64 except SR40 and SR52 were completely started or started to at least k=10000. Besides, all started k's for all extended Sierpinski/Riesel bases b<=64 were tested to at least n=1000.

sweety439 · 2017-05-05, 17:51

Quote:

Originally Posted by sweety439

Corrected the text files: Should list ",NA" instead of ",0". (the errors are in the text files for SR42 and SR60)

These text files do not include R3 and R6.

The R3 primes with k = 1 mod 2 and n>5000 are:

Code:

k       n
119     8972
313     24761
997     20847
3337    12083
4111    12978
5437    9567
6119    28580
6317    15331
6737    17455
7031    5898
7379    16856
7511    26022
7577    5031
8059    47256
8753    16533
9179    21404
9311    11134
11251   24314
11519   11140
11753   36665

The R6 primes with k = 1 mod 5 and n>2000 are:

Code:

k       n
251     3008
2626    27871
4241    7056
8331    10461
8786    4091
11061   3225
16101   4009
23031   11921
25166   2769
26461   11657
27901   2578
28846   2504
29266   3020
30161   2890
31606   2147
32451   3826
34021   5807
34831   6820
37876   8976
40636   18749
42216   2700
44386   3246
46096   4015
46441   3826
54536   24822
55826   5103
61426   5009
68186   2694
70216   3206
70706   2548
76796   10630
78541   2939

sweety439 · 2017-05-05, 18:20

Some bases and k's have algebra factors, but since for an n, one of these factors become 1 when divided by gcd(k+-1,b-1), so these bases and k's have a prime but they can only have this prime, thus they are excluded form the conjectures. These bases, k's and n's are: (for bases b<=64)

Code:

base    k    n
S8      27   1
S16     4    1
R4      1    2
R4      4    1
R8      1    3
R8      8    2
R16     1    2
R16     16   1
R27     1    3
R36     1    2
R36     36   1
R64     8    1

sweety439 · 2017-05-05, 18:33

Quote:

Originally Posted by sweety439

These text files do not include R3 and R6.

The R3 primes with k = 1 mod 2 and n>5000 are:

Code:

k       n
119     8972
313     24761
997     20847
3337    12083
4111    12978
5437    9567
6119    28580
6317    15331
6737    17455
7031    5898
7379    16856
7511    26022
7577    5031
8059    47256
8753    16533
9179    21404
9311    11134
11251   24314
11519   11140
11753   36665

The R6 primes with k = 1 mod 5 and n>2000 are:

Code:

k       n
251     3008
2626    27871
4241    7056
8331    10461
8786    4091
11061   3225
16101   4009
23031   11921
25166   2769
26461   11657
27901   2578
28846   2504
29266   3020
30161   2890
31606   2147
32451   3826
34021   5807
34831   6820
37876   8976
40636   18749
42216   2700
44386   3246
46096   4015
46441   3826
54536   24822
55826   5103
61426   5009
68186   2694
70216   3206
70706   2548
76796   10630
78541   2939

https://www.rose-hulman.edu/~rickert/Compositeseq/

This webpage has many errors for R3 and R6: (note that in this page, the "k" is (k-1)/2 for R3 k = 1 mod 2 and (k-1)/5 for R6 k = 1 mod 5)

* R3, k=7379, this page shows that this k has no prime with n<=19200, but it actually has a (probable) prime at n=16856.
* R6, k=491, this page shows that this k has a (probable) prime at n=3041, but it actually has a prime at n=3, but for k = 106056 = 491*6^3, this prime k=491, n=3 would be k=106056, n=0 but n must be > 0 hence it is not allowed so k=106056 must continue to be searched (if we also include the k's > CK, e.g. if we want to solve the 2nd, 3rd, 4th, ... conjecture), as this page shows, k=106056 has a (probable) prime at n=3038.
* R6, k=2876, this page shows that this k has a (probable) prime at n=6476, but it actually has a prime at n=2, but for k = 103536 = 2876*6^2, this prime k=2876, n=2 would be k=103536, n=0 but n must be > 0 hence it is not allowed so k=103536 must continue to be searched (if we also include the k's > CK, e.g. if we want to solve the 2nd, 3rd, 4th, ... conjecture), as this page shows, k=103536 has a (probable) prime at n=6474.

gd_barnes · 2017-05-05, 23:10

Quote:

Originally Posted by sweety439

https://www.rose-hulman.edu/~rickert/Compositeseq/

This webpage has many errors for R3 and R6: (note that in this page, the "k" is (k-1)/2 for R3 k = 1 mod 2 and (k-1)/5 for R6 k = 1 mod 5)

* R3, k=7379, this page shows that this k has no prime with n<=19200, but it actually has a (probable) prime at n=16856.
* R6, k=491, this page shows that this k has a (probable) prime at n=3041, but it actually has a prime at n=3, but for k = 106056 = 491*6^3, this prime k=491, n=3 would be k=106056, n=0 but n must be > 0 hence it is not allowed so k=106056 must continue to be searched, as this page shows, k=106056 has a (probable) prime at n=3038.
* R6, k=2876, this page shows that this k has a (probable) prime at n=6476, but it actually has a prime at n=2, but for k = 103536 = 2876*6^2, this prime k=2876, n=2 would be k=103536, n=0 but n must be > 0 hence it is not allowed so k=103536 must continue to be searched, as this page shows, k=103536 has a (probable) prime at n=6474.

Thanks for copying the errors that I previously posted in the "add repeated digits..." thread. :-(

That page also has a large number of errors for base 7 various digits. There were so many errors that I didn't want to list them all. You can compare my primes and k's remaining from the above thread to this old page for base 7. I suggest completely ignoring the page.

Why don't you create your own web page? You might get some searchers for this effort. Continually posting updated text files and links to other's old efforts is very poor presentation.

sweety439 · 2017-05-06, 14:40

Update the text file for the R3 primes for even k, if you need it.

There is no even k remain for R3.

For odd k, see the post #203.

sweety439 · 2017-05-06, 14:46

Quote:

Originally Posted by gd_barnes

Thanks for copying the errors that I previously posted in the "add repeated digits..." thread. :-(

That page also has a large number of errors for base 7 various digits. There were so many errors that I didn't want to list them all. You can compare my primes and k's remaining from the above thread to this old page for base 7. I suggest completely ignoring the page.

Why don't you create your own web page? You might get some searchers for this effort. Continually posting updated text files and links to other's old efforts is very poor presentation.

There is a word file about it, the format of this file is the same as that of the CRUS page, see the post #175.

sweety439 · 2017-05-06, 14:53

Quote:

Originally Posted by gd_barnes

Thanks for copying the errors that I previously posted in the "add repeated digits..." thread. :-(

That page also has a large number of errors for base 7 various digits. There were so many errors that I didn't want to list them all. You can compare my primes and k's remaining from the above thread to this old page for base 7. I suggest completely ignoring the page.

Why don't you create your own web page? You might get some searchers for this effort. Continually posting updated text files and links to other's old efforts is very poor presentation.

Can you reserve these problems (extended Sierpinski/Riesel problems)? Especially S3, S10, S25 and R7. The word file already give the list of the remain k's.

2017-05-05, 18:20	#204
sweety439 "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 2·13·113 Posts	Some bases and k's have algebra factors, but since for an n, one of these factors become 1 when divided by gcd(k+-1,b-1), so these bases and k's have a prime but they can only have this prime, thus they are excluded form the conjectures. These bases, k's and n's are: (for bases b<=64) Code: base k n S8 27 1 S16 4 1 R4 1 2 R4 4 1 R8 1 3 R8 8 2 R16 1 2 R16 16 1 R27 1 3 R36 1 2 R36 36 1 R64 8 1 Last fiddled with by sweety439 on 2017-05-05 at 18:21

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2017-05-05, 13:25	#202
sweety439 "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 2×13×113 Posts	Now, all extended Sierpinski/Riesel bases b<=64 except SR40 and SR52 were completely started or started to at least k=10000. Besides, all started k's for all extended Sierpinski/Riesel bases b<=64 were tested to at least n=1000.