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Forum: sweety439 2020-07-08, 18:16
Replies: 874
Views: 25,001
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: 874
Views: 25,001
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...
Forum: sweety439 2020-07-08, 18:05
Replies: 874
Views: 25,001
Posted By sweety439
Of course, * In the Riesel case if k and b...

Of course,

* In the Riesel case if k and b are both r-th powers for an r>1

* In the Sierpinski case if k and b are both r-th powers for an odd r>1

* In the Sierpinski case if k is of the...
Forum: sweety439 2020-07-08, 17:58
Replies: 874
Views: 25,001
Posted By sweety439
There are other k's excluded from the...

There are other k's excluded from the Riesel/Sierpinski problems (Riesel is still much more such k's)

* R30 k=1369:

for even n let n=2*q; factors to: (37*30^q - 1) * (37*30^q + 1)

odd n:...
Forum: sweety439 2020-07-08, 17:08
Replies: 874
Views: 25,001
Posted By sweety439
All n must be >= 1. All MOB k-values need an...

All n must be >= 1.

All MOB k-values need an n>=1 prime (unless they have a covering set of primes, or make a full covering set with all or partial algebraic factors)

MOB k-values such that...
Forum: Conjectures 'R Us 2020-07-08, 16:27
Replies: 17
Views: 494
Posted By sweety439
There is no known twin prime for some even k...

There is no known twin prime for some even k divisible by 3, e.g. k=312 (since all n must be >=1)
Forum: Miscellaneous Math 2020-07-08, 16:25
Replies: 10
Views: 152
Posted By sweety439
k*2^n+1 and k*2^(n+1)+1 can be both prime only...

k*2^n+1 and k*2^(n+1)+1 can be both prime only for k divisible by 3, or one of these two numbers will be divisible by 3.
Forum: sweety439 2020-07-07, 19:27
Replies: 874
Views: 25,001
Posted By sweety439
(79*73^9339-1)/6 is (probable) prime!!! R73...

(79*73^9339-1)/6 is (probable) prime!!!

R73 is proven!!!
Forum: sweety439 2020-07-07, 18:08
Replies: 874
Views: 25,001
Posted By sweety439
In fact, (k*b^n+1)/gcd(k+1,b-1) has algebra...

In fact, (k*b^n+1)/gcd(k+1,b-1) has algebra factors if and only if k*b^n is either perfect odd power or of the form 4*m^4, and (k*b^n-1)/gcd(k-1,b-1) has algebra factors if and only if k*b^n is...
Forum: sweety439 2020-07-07, 18:04
Replies: 874
Views: 25,001
Posted By sweety439
Checking whether a k-value makes a full covering...

Checking whether a k-value makes a full covering set with algebraic factors not always very easy. The way I do it is to look for patterns in the factors of the various n-values for specific k-values....
Forum: sweety439 2020-07-07, 09:32
Replies: 874
Views: 25,001
Posted By sweety439
https://docs.google.com/document/d/e/2PACX-1vR3ubC...

https://docs.google.com/document/d/e/2PACX-1vR3ubC0-QCspbRFX-YnLRxPLm_Y448tN8BkLjyIeKsVYbb7EOrLYhw5tw6T-LV6SPlXLCncZ4OqEDGd/pub

Newest status of Riesel problems
Forum: sweety439 2020-07-07, 09:24
Replies: 874
Views: 25,001
Posted By sweety439
(101*73^2146-1)/4 is (probable) prime!!! R73...

(101*73^2146-1)/4 is (probable) prime!!!

R73 has only k=79 remain, reserve it to n=10K
Forum: sweety439 2020-07-07, 09:01
Replies: 874
Views: 25,001
Posted By sweety439
So far, there is only two Riesel k and base <=...

So far, there is only two Riesel k and base <= 128 where algebraic factors on even-n combine with a covering set of MORE than one factor on odd-n to eliminate a k. That is 1369*30^n-1 and...
Forum: sweety439 2020-07-07, 08:43
Replies: 874
Views: 25,001
Posted By sweety439
Exclusions: k's that are multiples of the...

Exclusions:

k's that are multiples of the base where (k+-1)/gcd(k+-1,b-1) (+ for Sierp, - for Riesel) is not prime.

I'll give some examples for S22:

k=44, 154, 220, 242, 264, 374, 440 would...
Forum: sweety439 2020-07-07, 08:19
Replies: 874
Views: 25,001
Posted By sweety439
A Sierpinski form (k*b^n+1)/gcd(k+1,b-1) has...

A Sierpinski form (k*b^n+1)/gcd(k+1,b-1) has algebra factors if and only if k*b^n is perfect odd power A070265 (https://oeis.org/A070265) or of the form 4*m^4 A101046 (https://oeis.org/A141046)

A...
Forum: sweety439 2020-07-07, 08:10
Replies: 874
Views: 25,001
Posted By sweety439
Any Riesel k that is a perfect square will always...

Any Riesel k that is a perfect square will always be lower weight than average because the even-n have algebraic factors.
Forum: Prime Wiki 2020-07-07, 07:36
Replies: 176
Sticky: Prime-Wiki
Views: 12,903
Posted By sweety439
The "twin prime pair" is a Riesel prime and a...

The "twin prime pair" is a Riesel prime and a Proth prime with the same values of k and n, but the wiki only has category "Riesel prime without twin" and does not have category "Proth prime with...
Forum: sweety439 2020-07-07, 04:45
Replies: 3
Views: 18
Posted By sweety439
I conjectured that all numbers > 127 satisfy at...

I conjectured that all numbers > 127 satisfy at most one of the three criteria.
Forum: sweety439 2020-07-07, 04:41
Replies: 3
Views: 18
Posted By sweety439
I think it is not prime because it is...

I think it is not prime because it is corresponding to the number 5

Like the case of Fermat numbers:

F0=3 is prime, F1=5 is prime, F2=17 is prime, F3=257 is prime, F4=65537 is prime, but...
Forum: sweety439 2020-07-06, 18:22
Replies: 3
Views: 18
Posted By sweety439
Some other conjectures

I conjectured that 127 (not M127) is the largest number satisfying all three conditions in New Mersenne (Wagstaff) conjecture.

Also, how about test whether the numbers MW127 and WW127 is prime?...
Forum: Conjectures 'R Us 2020-07-06, 17:00
Replies: 1,663
Views: 102,917
Posted By sweety439
The "top 10 primes" for R55 has the prime...

The "top 10 primes" for R55 has the prime 68*55^29173-1, however, 68*55^1-1 = 3739 is prime, thus this prime is not the first prime for k=68
Forum: sweety439 2020-07-05, 16:11
Replies: 874
Views: 25,001
Posted By sweety439
We don't know the conjectures yet on bases 66,...

We don't know the conjectures yet on bases 66, 120, 156, 180, 210, 240, 280, 330, 358, 420, 456, 462, 546, ... and Sierp 190, 540 and Riesel 276, 486. They are definitely k > 1M. They're just too...
Forum: sweety439 2020-07-05, 14:36
Replies: 358
Views: 9,796
Posted By sweety439
Update files

Update files
Forum: sweety439 2020-07-04, 16:15
Replies: 874
Views: 25,001
Posted By sweety439
These Sierpinski bases (up to 1024) cannot be...

These Sierpinski bases (up to 1024) cannot be proven with current knowledge and technology, since they have either GFN (for even bases) or half GFN (odd bases) remain: (half GFN is much worse, since...
Forum: sweety439 2020-07-04, 16:09
Replies: 874
Views: 25,001
Posted By sweety439
k is Riesel number base b if.... k ...

k is Riesel number base b if....


k b
1 (none)
2 (none)
3 (none)
4 == 14 mod 15
5 == 11 mod 12
6 == 34 mod 35
Showing results 1 to 25 of 1000

 
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