[QUOTE=sweety439;559581]k-values that are a multiple of base (b) and where (k+-1)/gcd(k+-1,b-1) (+ for Sierpinski, - for Riesel) is not prime are included in the conjectures but excluded from testing, since such k-values will have the same prime as k / b.

However, k-values that are a multiple of base (b) and where (k+-1)/gcd(k+-1,b-1) (+ for Sierpinski, - for Riesel) is prime are included from testing since the exponent n must be >=1 (n can be 1, but cannot be 0 or -1 or -2 or ...), and the same prime n=1 for k / b would be n=0 for this k but n must be >=1 hence it is not allowed so this k must continue to be searched. (of course, k-values that are not a multiple of base (b) are included from testing)

Thus, for S3, k = 42, 45, 57, 60, 66 and 72 are included from testing since although 42, 45, 57, 60, 66 and 72 are multiples of 3, but 42+1, (45+1)/2, (57+1)/2, 60+1, 66+1 and 72+1 are primes. However, k = 48, 51, 54, 63, 69 and 75 are excluded from testing since 48, 51, 54, 63, 69 and 75 are multiples of 3, and 48+1, (51+1)/2, 54+1, (63+1)/2, (69+1)/2 and (75+1)/2 are not primes. Besides, for R3, k = 42, 48, 54, 60, 63, 72 and 75 are included from testing since although 42, 48, 54, 60, 63, 72 and 75 are multiples of 3, but 42-1, 48-1, 54-1, 60-1, (63-1)/2, 72-1 and (75-1)/2 are primes. However, k = 45, 51, 57, 66 and 69 are excluded from testing since 45, 51, 57, 66 and 69 are multiples of 3, and (45-1)/2, (51-1)/2, (57-1)/2, 66-1 and (69-1)/2 are not primes.

Note: Since 1 is not prime, thus for R3, k = 3 is excluded from testing. ((3-1)/2 = 1) However, since 2 is prime, thus for S3, k = 3 is included from testing. ((3+1)/2 = 2)[/QUOTE]

Since 1 is not prime, thus for a Riesel base b>=2, k = b is excluded from testing since (b-1)/gcd(b-1,b-1) = (b-1)/(b-1) = 1, thus k = b would have the same prime as k = 1.

The formula for Sierpinski conjectures in CRUS is k*b^n+1
The formula for Riesel conjectures in CRUS is k*b^n-1
The formula for Sierpinski conjectures in this project is (k*b^n+1)/gcd(k+1,b-1)
The formula for Riesel conjectures in this project is (k*b^n-1)/gcd(k-1,b-1)

All n must be >= 1.

k-values which make a full covering set with all or partial algebraic factors are excluded from the conjectures.

k-values that are a multiple of base (b) and where (k+-1)/gcd(k+-1,b-1) (+ for Sierpinski, - for Riesel) is not prime are included in the conjectures but excluded from testing. Such k-values will have the same prime as k / b.

[QUOTE=sweety439;559245]The CK for S726 is known to be 10923176
The CK for R726 is known to be 12751579[/QUOTE]

The CK for S1020 is known to be 95696289
The CK for R1020 is known to be 94655888

[QUOTE=sweety439;559720]The CK for S1020 is known to be 95696289
The CK for R1020 is known to be 94655888[/QUOTE]

I skipped bases 876 and 966 because the covering of the upper bound of these two bases (except the Riesel sides of 966) have a prime > 50000:

S876 and R876 have 59029
S966 has 71707

Like the status for both sides for base 728, which has 105997

Now, the CK for all Sierpinski/Riesel bases <= 1024 except SR156, SR280, SR876, SR910, R946, SR960, SR966 (which have too large upper bounds) are known!!!

See [URL="https://github.com/xayahrainie4793/Extended-Sierpinski-Riesel-conjectures/blob/master/Sierpinski%20CK%20for%20bases%20up%20to%202048.txt"]https://github.com/xayahrainie4793/Extended-Sierpinski-Riesel-conjectures/blob/master/Sierpinski%20CK%20for%20bases%20up%20to%202048.txt[/URL] (Sierpinski) and [URL="https://github.com/xayahrainie4793/Extended-Sierpinski-Riesel-conjectures/blob/master/Riesel%20CK%20for%20bases%20up%20to%202048.txt"]https://github.com/xayahrainie4793/Extended-Sierpinski-Riesel-conjectures/blob/master/Riesel%20CK%20for%20bases%20up%20to%202048.txt[/URL] (Riesel) for the CK's for bases 2 <= b <= 2500 and b = 4096, 8192, 16384, 32768, 65536

This is the sieve file for R70

[QUOTE=sweety439;555862]2 (probable) primes found for R70:

(376*70^6484-1)/3
(496*70^4934-1)/3

k=811 still remains ....[/QUOTE]

No other (probable) primes found for R70 k = 376, 496, 811 up to n=22813

[QUOTE=sweety439;558877]This including:

* k=1 for all Sierpinski base not of the form m^r with odd r>1 nor of the form 4*m^4
* k=1 for all Riesel base not of the form m^r with r>1
* k=2 for all Sierpinski base not == 2 mod 3
* k=2 for all Sierpinski base of the form 2^r-2 or 3*2^r-2
* k=2 for all Riesel base
* k=3 for all Sierpinski base not == 3 mod 4
* k=3 for all Sierpinski base of the form 3^r-3 or 2*3^r-3 or 4*3^r-3
* k=3 for all Riesel base
* k=5 for all Sierpinski base not == 2 mod 3
* k=5 for all Sierpinski base of the form 5^r-5 or 2*5^r-5 or 3*5^r-5 or 6*5^r-5
* k=5 for all Riesel base not == 3 mod 4
* k=5 for all Riesel base of the form 5^r+5 or 2*5^r+5 or 4*5^r+5
* k=6 for all Sierpinski base == 0, 1 mod 7
* k=6 for all Sierpinski base of the form 2^r*3^s-6 or 7*2^r*3^s-6
* k=6 for all Riesel base == 0, 1 mod 5
* k=6 for all Riesel base of the form 2^r*3^s+6 or 5*2^r*3^s+6
* k=7 for all Sierpinski base not == 3, 5, 7 mod 8
* k=7 for all Sierpinski base of the form 7^r-7 or 2*7^r-7 or 3*7^r-7 or 6*7^r-7
* k=7 for all Riesel base not == 2 mod 3
* k=7 for all Riesel base of the form 7^r+7 or 2*7^r+7 or 4*7^r+7 or 8*7^r+7
* k=b-2 for all Sierpinski base b where k is not of the form m^r with odd r>1 nor of the form 4*m^4
* k=b-2 for all Riesel base b
* k=b-1 for all Sierpinski base b where k is not of the form m^r with odd r>1 nor of the form 4*m^4
* k=b-1 for all Riesel base b
* k=b+1 for all Riesel base b
* k=b+2 for all Riesel base b[/QUOTE]

This also including all k-values such that k+-1 (+ for Sierpinski, - for Riesel) divides (b-1)*b^r for some r

[QUOTE=sweety439;560186]This also including all k-values such that k+-1 (+ for Sierpinski, - for Riesel) divides (b-1)*b^r for some r[/QUOTE]

Also all k-values such that numerator(k*b^n+-1) (+ for Sierpinski, - for Riesel) divides (b-1)*b^r for some (positive or negative or 0) integer n and (positive or 0) integer r