[QUOTE=sweety439;455376]Completed extended R36 for k<=10000 (tested to n=1000).[/QUOTE]

The remain k's <= 10000 for R36 are: (include the k's without from testing)

[FONT=&quot]251, 260, [/FONT][FONT=&quot]924, 1148, 1356, 1555, 1923, 2110, 2133, 2443, 2753, 2776, 3181, 3590, 3699, 3826, 3942, 4241, 4330, 4551, 4635, 4737, 4865, 5027, 5196, 5339, 5483, 5581, 5615, 5791, 5853, 6069, 6236, 6542, 6581, 6873, 6883, 7101, 7253, 7316, 7362, 7399, 7445, 7617, 7631, 7991, 8250, 8259, 8321, 8361, 8363, 8472, 8696, 9036, 9140, 9156, 9201, 9360, 9469, 9491, 9582[/FONT]

[QUOTE=sweety439;460867]The remain k's <= 10000 for R36 are: (include the k's without from testing)

[FONT=&quot]251, 260, [/FONT][FONT=&quot]924, 1148, 1356, 1555, 1923, 2110, 2133, 2443, 2753, 2776, 3181, 3590, 3699, 3826, 3942, 4241, 4330, 4551, 4635, 4737, 4865, 5027, 5196, 5339, 5483, 5581, 5615, 5791, 5853, 6069, 6236, 6542, 6581, 6873, 6883, 7101, 7253, 7316, 7362, 7399, 7445, 7617, 7631, 7991, 8250, 8259, 8321, 8361, 8363, 8472, 8696, 9036, 9140, 9156, 9201, 9360, 9469, 9491, 9582[/FONT][/QUOTE]

The k's from the same family are:

{251, 9036}
{260, 9360}

Thus, the remain k<=10000 for R36 are: (totally 59 k's)

[FONT=&quot]251, 260, [/FONT][FONT=&quot]924, 1148, 1356, 1555, 1923, 2110, 2133, 2443, 2753, 2776, 3181, 3590, 3699, 3826, 3942, 4241, 4330, 4551, 4635, 4737, 4865, 5027, 5196, 5339, 5483, 5581, 5615, 5791, 5853, 6069, 6236, 6542, 6581, 6873, 6883, 7101, 7253, 7316, 7362, 7399, 7445, 7617, 7631, 7991, 8250, 8259, 8321, 8361, 8363, 8472, 8696, 9140, 9156, 9201, 9469, 9491, 9582[/FONT]

[QUOTE=kar_bon;460762]No, I thought it was clear, I got my own work: 158 hours of my work here and you're unable to run WinPFGW?

You're testing to n~1500, which is done in seconds with pfgw. I don't know which program you're using so how much can you/we trust your results.

Notes:
- Stop posting tons of files and posts with pages of numbers, update the Wiki pages instead.
- You gave some values in bold, but nowhere explained the meaning.
- Change the display style of the table like [URL="http://www.mersennewiki.org/index.php/User:Karbon/S-Test"]this[/URL]: it's more compact and easier to watch
- Give the GCD for every k-val (I know it's easy to calculate, but noone will do this for many k-values, see example for base 2 & 3)
- Put more own work on current given values instead of creating more new conjectures (2nd, 3rd, 4th CK).[/QUOTE]

The format of the tables in [URL="http://www.mersennewiki.org/index.php/Sierpinski_problem_%28extended_definition%29"]http://www.mersennewiki.org/index.php/Sierpinski_problem_%28extended_definition%29[/URL] and [URL]http://www.mersennewiki.org/index.php/Riesel_problem_%28extended_definition%29[/URL] are completely the same as that in CRUS, i.e. that in [URL]http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm[/URL] and [URL]http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm[/URL].

[QUOTE=kar_bon;460762]No, I thought it was clear, I got my own work: 158 hours of my work here and you're unable to run WinPFGW?

You're testing to n~1500, which is done in seconds with pfgw. I don't know which program you're using so how much can you/we trust your results.

Notes:
- Stop posting tons of files and posts with pages of numbers, update the Wiki pages instead.
- You gave some values in bold, but nowhere explained the meaning.
- Change the display style of the table like [URL="http://www.mersennewiki.org/index.php/User:Karbon/S-Test"]this[/URL]: it's more compact and easier to watch
- Give the GCD for every k-val (I know it's easy to calculate, but noone will do this for many k-values, see example for base 2 & 3)
- Put more own work on current given values instead of creating more new conjectures (2nd, 3rd, 4th CK).[/QUOTE]

Oh, I will not create any new conjecture, but I hope that some people will solve all the existing conjectures in [URL]http://www.mersennewiki.org/index.php/Sierpinski_problem_%28extended_definition%29[/URL] and [URL]http://www.mersennewiki.org/index.php/Riesel_problem_%28extended_definition%29[/URL], e.g. S10 and S25, thus you can reserve S10 k=269 and S25 k=71.

The power of 2 bases are extended to base 1024 = 2^10.

These are the text file for the status for S256, S512 and S1024.

Also the text file for all CK for all power of 2 bases b <= 1024.

The CK for all power of 2 bases b <= 1024 are:

[CODE]
base CK
S2 78557
S4 419
S8 47
S16 38
S32 10
S64 14
S128 44
S256 38
S512 18
S1024 81
[/CODE][CODE]
base CK
R2 509203
R4 361
R8 14
R16 100
R32 10
R64 14
R128 44
R256 100
R512 14
R1024 81
[/CODE]The remain k's for these bases are:

[CODE]
base remain k
S256 11
S512 2, 4, 5, 16
S1024 4, 16, 29, 38, 44, 56
[/CODE]Note:

For S256, all k = 4*m^4 proven composite by full algebra factors.
For S512, all k = m^3 proven composite by full algebra factors.
For S1024, all k = m^5 proven composite by full algebra factors.

The prime (23*256^537+1)/3 (S256, k=23) is converted by S16, k=23.

Some test limits converted by CRUS:

S512, k=5: at n=1M.

Some test limits converted by GFN stats:

S512, k=2: at n=(2^54-1)/9-1
S512, k=4: at n=(2^49-2)/9-1
S512, k=16: at n=(2^44-4)/9-1
S1024, k=4: at n=(2^33-2)/10-1
S1024, k=16: at n=(2^34-4)/10-1

These are the text files for R256, R512 and R1024.


The remain k's for these bases are:

[CODE]
base remain k
R256 none (proven)
R512 none (proven)
R1024 13, 29, 31, 43, 56, 61
[/CODE]Note:

For R256, all k = m^2 proven composite by full algebra factors.
For R512, all k = m^3 proven composite by full algebra factors.
For R1024, all k = m^2 and all k = m^5 proven composite by full algebra factors.

The prime 4*512^2215-1 (R512, k=4) is given by CRUS.
The prime 13*512^2119-1 (R512, k=13) is given by CRUS.
The prime 39*1024^4070-1 (R1024, k=39) is given by CRUS.
The prime 74*1024^666084-1 (R1024, k=74) is given by CRUS.

Some test limits converted by CRUS:

R1024, k=29: at n=1M.

A k is included in the conjecture if and only if this k has infinitely many prime candidates.

Thus, although these k's have a prime, they are excluded from the conjectures:

S8, k=27: Although (27*8^1+1)/gcd(27+1,8-1) is prime, but (27*8^n+1)/gcd(27+1,8-1) is prime [I][B]only for[/B][/I] n=1, because of the algebra factors, thus k=27 is excluded from S8.

S16, k=4: Although (4*16^1+1)/gcd(4+1,16-1) is prime, but (4*16^n+1)/gcd(4+1,16-1) is prime [I][B]only for[/B][/I] n=1, because of the algebra factors, thus k=4 is excluded from S16.

R4, k=1: Although (1*4^2-1)/gcd(1-1,4-1) is prime, but (1*4^n-1)/gcd(1-1,4-1) is prime [I][B]only for[/B][/I] n=2, because of the algebra factors, thus k=1 is excluded from R4.

R4, k=4: Although (4*4^1-1)/gcd(4-1,4-1) is prime, but (4*4^n-1)/gcd(4-1,4-1) is prime [I][B]only for[/B][/I] n=1, because of the algebra factors, thus k=4 is excluded from R4.

R8, k=1: Although (1*8^3-1)/gcd(1-1,8-1) is prime, but (1*8^n-1)/gcd(1-1,8-1) is prime [I][B]only for[/B][/I] n=3, because of the algebra factors, thus k=1 is excluded from R8.

R8, k=8: Although (8*8^2-1)/gcd(8-1,8-1) is prime, but (8*8^n-1)/gcd(8-1,8-1) is prime [I][B]only for[/B][/I] n=2, because of the algebra factors, thus k=8 is excluded from R8.

R8, k=64: Although (64*8^1-1)/gcd(64-1,8-1) is prime, but (64*8^n-1)/gcd(64-1,8-1) is prime [I][B]only for[/B][/I] n=1, because of the algebra factors, thus k=64 is excluded from R8.

R16, k=1: Although (1*16^2-1)/gcd(1-1,16-1) is prime, but (1*16^n-1)/gcd(1-1,16-1) is prime [I][B]only for[/B][/I] n=2, because of the algebra factors, thus k=1 is excluded from R16.

R16, k=16: Although (16*16^1-1)/gcd(16-1,16-1) is prime, but (16*16^n-1)/gcd(16-1,16-1) is prime [I][B]only for[/B][/I] n=1, because of the algebra factors, thus k=16 is excluded from R16.

etc.

Non-certified probable prime exists only if gcd(k+-1,b-1) (+ for Sierpinski, - for Riesel) is not 1.

If gcd(k+-1,b-1) = 1 (+ for Sierpinski - for Riesel), then the prime for this k and this base b for this problem (the extended Sierpinski/Riesel problem) is the same as the prime for this k and this base b for the original Sierpinski/Riesel problem (the problem in CRUS).

In the Riesel case, if k=1, then this problem is completely the same as finding the smallest generalized repunit prime in base b (b should be a non-perfect power, or it would have algebra factors).

For more information for this problem (finding the smallest generalized repunit prime in base b), see [URL]http://oeis.org/A084740[/URL] and the thread [URL]http://mersenneforum.org/showthread.php?t=21808[/URL].

SR108 were done, tested to n=1000, only tested the k's not in CRUS (i.e. k's such that gcd(k+-1,b-1) is not 1).

The remain k for S108 with k = 106 mod 107 are {8987, 14444, 18831, 20543, 21613}

The remain k for R108 with k = 1 mod 107 are {3532, 5351, 6528, 13162}