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Forum: sweety439 2020-07-12, 19:47
Replies: 900
Views: 25,758
Posted By sweety439
These bases b have many small Sierpinski/Riesel...

These bases b have many small Sierpinski/Riesel numbers k:


base Sierpinski numbers k Riesel numbers k
5 == 7, 11 mod 24 == 13, 17 mod 24...
Forum: sweety439 2020-07-12, 19:16
Replies: 900
Views: 25,758
Posted By sweety439
and such k's are square numbers k such that the...

and such k's are square numbers k such that the highest power of 2 dividing (k-1) is the same as the highest power of 2 dividing (b-1)

(not consider the case that b is square, since any square k...
Forum: sweety439 2020-07-12, 19:14
Replies: 900
Views: 25,758
Posted By sweety439
Thus, the second case (i.e. has algebra factors...

Thus, the second case (i.e. has algebra factors for even n and divisible by 2 for odd n) only exists for bases b == 1 mod 8
Forum: sweety439 2020-07-12, 18:54
Replies: 900
Views: 25,758
Posted By sweety439
If gcd(k+-1,b-1) = 1 (+ for Sierpinski, - for...

If gcd(k+-1,b-1) = 1 (+ for Sierpinski, - for Riesel), then this is completely the same as the Sierpinski/Riesel problem in CRUS for this (k,b) combo, these Sierpinski/Riesel problems just extend the...
Forum: sweety439 2020-07-12, 18:50
Replies: 900
Views: 25,758
Posted By sweety439
Since a large probable prime n can be proven to...

Since a large probable prime n can be proven to be prime if and only if at least one of n-1 and n+1 can be trivially written into a product.

Thus, if n is large, a probable prime...
Forum: sweety439 2020-07-12, 18:49
Replies: 900
Views: 25,758
Posted By sweety439
For Sierpinski side: Case gcd(k+1,b-1) = 1...

For Sierpinski side:

Case gcd(k+1,b-1) = 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...
Forum: sweety439 2020-07-12, 18:42
Replies: 900
Views: 25,758
Posted By sweety439
However, there are cases that cannot have prime: ...

However, there are cases that cannot have prime:

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,...
Forum: sweety439 2020-07-12, 18:35
Replies: 900
Views: 25,758
Posted By sweety439
Why shouldn't I do this?

Why shouldn't I do this?
Forum: sweety439 2020-07-12, 16:06
Replies: 900
Views: 25,758
Posted By sweety439
Also these cases: S15 k=343: since 343...

Also these cases:

S15 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,...
Forum: sweety439 2020-07-12, 15:18
Replies: 900
Views: 25,758
Posted By sweety439
The only exception of "there must be a prime at...

The only exception of "there must be a prime at some point" is the case in post #265 (https://mersenneforum.org/showpost.php?p=459405&postcount=265)
Forum: sweety439 2020-07-12, 15:15
Replies: 900
Views: 25,758
Posted By sweety439
Also, For Riesel side...

Also,

For Riesel side ((k*b^n-1)/gcd(k-1,b-1)), if k*b^s is r-th power with prime r, then all n == s mod r have algebra factors, and we only want to know whether it has a covering set of primes...
Forum: sweety439 2020-07-12, 15:14
Replies: 900
Views: 25,758
Posted By sweety439
For Riesel side ((k*b^n-1)/gcd(k-1,b-1)), if k is...

For Riesel side ((k*b^n-1)/gcd(k-1,b-1)), if k is r-th power with prime r, then all n divisible by r have algebra factors, and we only want to know whether it has a covering set of primes for all n...
Forum: sweety439 2020-07-11, 19:51
Replies: 900
Views: 25,758
Posted By sweety439
Also, if k*b is square and k*b == -1...

Also,

if

k*b is square and k*b == -1 mod p and b == -1 mod p for some odd prime p (this situation only exists for p == 1 mod 4)

or

k*b is square and k*b == 2^(r-1)+1 mod 2^r and b ==...
Forum: sweety439 2020-07-11, 19:45
Replies: 900
Views: 25,758
Posted By sweety439
If k is square and k == -1 mod p and b == -1...

If

k is square and k == -1 mod p and b == -1 mod p for some odd prime p (this situation only exists for p == 1 mod 4)

or

k is square and k == 2^(r-1)+1 mod 2^r and b == 2^(r-1)+1 mod 2^r for...
Forum: sweety439 2020-07-11, 17:30
Replies: 900
Views: 25,758
Posted By sweety439
Update newest status of Sierpinski problems...

Update newest status of Sierpinski problems (https://docs.google.com/document/d/e/2PACX-1vQ96fx2qG6Gqfp56Z66Yqy3bPQhMZ0SI_7iGmmMO4oXiwusyjRcihnROLwg2uPHHv4mo7yKpahXG1PL/pub)

(S53 and S122)
Forum: Conjectures 'R Us 2020-07-11, 16:59
Replies: 2,114
Views: 136,527
Posted By sweety439
Nice!!! This base become the 1k Sierp base with...

Nice!!! This base become the 1k Sierp base with highest CK (22413) :bow wave::bow wave: (and the 1k base with 3rd highest CK, the 1st and 2nd are R31 (134718) and R6 (84687)
Forum: sweety439 2020-07-10, 18:47
Replies: 900
Views: 25,758
Posted By sweety439
These k's cannot have any algebra factors since...

These k's cannot have any algebra factors since there is no n such that 47*15^n (or 257*33^n, 1555*36^n) is perfect power, however, we can check whether a k-value makes a full covering set with...
Forum: sweety439 2020-07-10, 17:43
Replies: 900
Views: 25,758
Posted By sweety439
Such situation also exists for Sierpinski k=324: ...

Such situation also exists for Sierpinski k=324:

These bases have (odd n has factor of 19 and n == 2 mod 4 has factor of 17):

132, 208, 455, 531, 778, 854, 1101, 1177, 1424, 1500, 1747, 1823,...
Forum: sweety439 2020-07-10, 17:41
Replies: 900
Views: 25,758
Posted By sweety439
Sierpinski k=2500 also for these square bases, in...

Sierpinski k=2500 also for these square bases, in square bases, all even n have algebra factors, and for these bases (square of numbers == 4 or 13 mod 17) all odd n have factor of 17:

16, 169,...
Forum: sweety439 2020-07-10, 17:18
Replies: 900
Views: 25,758
Posted By sweety439
Also, for Sierpinski k=2500 (while n == 0 mod 4...

Also, for Sierpinski k=2500 (while n == 0 mod 4 have algebra factors)

These bases have (odd n has factor of 3 and n == 2 mod 4 has factor of 17):

38, 47, 89, 98, 140, 149, 191, 200, 242, 251,...
Forum: sweety439 2020-07-10, 17:08
Replies: 900
Views: 25,758
Posted By sweety439
There are many Riesel case for k=64 (since 64 =...

There are many Riesel case for k=64 (since 64 = 4^3 = 8^2, thus n == 0 mod 2 or n == 0 mod 3 have algebra factors:

Bases 619, 1322, 2025, 2728, 3431, 4134, 4837, 5540, 6243, 6946, 7649, 8352,...
Forum: sweety439 2020-07-10, 16:35
Replies: 900
Views: 25,758
Posted By sweety439
Update newest status ...

Update newest status

https://docs.google.com/document/d/e/2PACX-1vTXTyZ33khd1EtCiU2_PKKAwDEezH8nOMmCL71ZBAGJfVfD_wJlhLkKbIGBCbSxzvZVUm8HDWrvEC82/pub
Forum: sweety439 2020-07-10, 06:31
Replies: 900
Views: 25,758
Posted By sweety439
See...

See https://en.wikipedia.org/w/index.php?title=Wikipedia:Sandbox&oldid=966555963
Forum: sweety439 2020-07-08, 18:16
Replies: 900
Views: 25,758
Posted By sweety439
Also, in the Sierpinski case if b = q^m, k = q^r,...

Also, in the Sierpinski case if b = q^m, k = q^r, where q is not of the form t^s with odd s>1, and m and r have no common odd prime factor, and the exponent of highest power of 2 dividing r >= the...
Forum: sweety439 2020-07-08, 18:10
Replies: 900
Views: 25,758
Posted By sweety439
The k's that make a full covering set with all or...

The k's that make a full covering set with all or partial algebraic factors are excluded from the conjectures, unless they also have a covering set of primes (e.g. R4 k=361, R8 k=343, R9 k=49, R16...
Showing results 1 to 25 of 1000

 
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