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Forum: Conjectures 'R Us 2020-03-27, 15:51
Replies: 32
Views: 1,283
Posted By sweety439
Well... since all prime factors of k*2^n+-1 are...

Well... since all prime factors of k*2^n+-1 are odd, thus if there exist an n such that k*2^n+-1 or its dual (|2^n+-k|) is power of 2 (including 1), then k*2^n+-1 cannot have a covering set.

Thus...
Forum: Conjectures 'R Us 2020-03-27, 15:45
Replies: 32
Views: 1,283
Posted By sweety439
9*1024^n-1 is unlikely to have a covering set,...

9*1024^n-1 is unlikely to have a covering set, like the simple cases: 3*2^n+-1, 5*2^n+-1, 7*2^n+-1, 9*2^n+-1, 11*2^n+-1, etc. they are unlikely to have a covering set, but also no proof.
Forum: Conjectures 'R Us 2020-03-27, 15:43
Replies: 32
Views: 1,283
Posted By sweety439
This is like the base 125 case, the CK for both...

This is like the base 125 case, the CK for both sides of base 125 are 8, and both 125 and 8 are cubes, thus 8*125^n+-1 both have algebra factors.
Forum: Conjectures 'R Us 2020-03-27, 14:48
Replies: 32
Views: 1,283
Posted By sweety439
An example is Sierp base 311, all k's that...

An example is Sierp base 311, all k's that between a multiple of 3 and a multiple of 13 have the covering set {3,13}, the first such k's are 14, 25, 53, 64, 92, 103, 131, 142, ..., however all such...
Forum: Conjectures 'R Us 2020-03-10, 21:45
Replies: 832
Views: 55,806
Posted By sweety439
A nice prime for k=7!!!

A nice prime for k=7!!!
Forum: Conjectures 'R Us 2020-03-10, 21:44
Replies: 2,070
Views: 128,750
Posted By sweety439
8*283^164768-1 is prime, see post...

8*283^164768-1 is prime, see post https://mersenneforum.org/showpost.php?p=537817&postcount=105
Forum: sweety439 2020-03-06, 18:13
Replies: 693
Views: 18,978
Posted By sweety439
Pairs of S/R bases: 33 through 64: SR40...

Pairs of S/R bases:

33 through 64:

SR40 vs SR52

SR42 vs SR60 (not SR48, because 48+-1 are not both primes)

SR46 vs SR58
Forum: enzocreti 2020-02-17, 16:13
Replies: 5
Views: 294
Posted By sweety439
Well, since the Nash weight of (k,b,c) = (1,56,1)...

Well, since the Nash weight of (k,b,c) = (1,56,1) is low (if a triple (k,b,c) does not satisfy all four conditions, then the Nash weight of this (k,b,c) triple is 0).
Forum: And now for something completely different 2020-02-17, 16:10
Replies: 4
Views: 1,214
Posted By sweety439
Can someone reserve (51^4229-1)/50,...

Can someone reserve (51^4229-1)/50, (91^4421-1)/90 and 60^4663-59^4663?
Forum: enzocreti 2020-02-17, 15:58
Replies: 5
Views: 294
Posted By sweety439
In your case is (k,b,c) = (1,56,1), satisfying...

In your case is (k,b,c) = (1,56,1), satisfying all four conditions, thus I conjectured that there are infinitely many primes of this form, additionally, I conjectured that there are infinitely many...
Forum: enzocreti 2020-02-17, 15:56
Replies: 5
Views: 294
Posted By sweety439
See post...

See post https://mersenneforum.org/showpost.php?p=529838&postcount=675, I conjectured that there are infinitely many integers n>=1 such that (k*b^n+c)/gcd(k+c, b-1) is prime for all integer triples...
Forum: sweety439 2020-02-14, 13:06
Replies: 4
Views: 345
Posted By sweety439
Always composite numbers?

Can a dozenal (duodecimal, base 12) number {111...111}21{111...111} (with the same number of 1s in the two brackets) (start with 21, 1211, 112111, 11121111, ...) be prime? I cannot find such prime...
Forum: Riesel Prime Search 2020-02-14, 12:30
Replies: 0
Views: 168
Posted By sweety439
How do we calculate the weight?

How do we calculate the weight for a form (k*b^n+c)/gcd(k+c,b-1) for fixed integers k >= 1, b >= 2, c != 0, gcd(k,c) = 1, gcd(b,c) = 1.

I have a research...
Forum: enzocreti 2020-02-14, 12:23
Replies: 2
Views: 148
Posted By sweety439
Yes!!! 43^3*127^3+1 is.

Yes!!! 43^3*127^3+1 is.
Forum: enzocreti 2020-02-14, 12:21
Replies: 3
Views: 200
Posted By sweety439
Wait!!! 47%41 = 6, and 6 is not perfect...

Wait!!! 47%41 = 6, and 6 is not perfect power....:poop::poop:
Forum: enzocreti 2020-02-14, 12:20
Replies: 3
Views: 200
Posted By sweety439
Of course!!! By Dirichlet's theorem on arithmetic...

Of course!!! By Dirichlet's theorem on arithmetic progressions, there are infinitely many primes = 4 mod 41, thus there are infinitely many such primes.
Forum: enzocreti 2020-02-14, 12:18
Replies: 3
Views: 222
Posted By sweety439
There is a formula of repunits mod p for prime p,...

There is a formula of repunits mod p for prime p, the period must be a factor of p-1, thus, you can only calculate R1%p, R2%p, R3%p, ..., R(p-1)%p
Forum: enzocreti 2020-02-14, 12:15
Replies: 10
Views: 429
Posted By sweety439
powerpi(x)=floor(x^(1/2))+floor(x^(1/3))+floor(x^(...

powerpi(x)=floor(x^(1/2))+floor(x^(1/3))+floor(x^(1/5))+floor(x^(1/7))+floor(x^(1/11))+...

e.g. powerpi(9453)=97+21+6+3+2+2=131
Forum: sweety439 2020-02-11, 11:08
Replies: 7
Views: 404
Posted By sweety439
This test always uses base 2 for the Fermat test...

This test always uses base 2 for the Fermat test part, but I use the base which is the smallest integer b>=2 such that JacobiSymbol(b,n) = -1

Thus, this test not the same as my test.

Edit: n...
Forum: sweety439 2020-02-11, 11:05
Replies: 159
Views: 7,909
Posted By sweety439
You are really searching the generalized repunit...

You are really searching the generalized repunit (probable) primes, see https://oeis.org/history?user=Paul%20Bourdelais, you found the PRPs (3^1896463+1)/4, (6^1365019-1)/5, and (37^168527-1)/36...
Forum: Lounge 2020-02-11, 11:00
Replies: 116
Sticky: Predict M52
Views: 7,581
Posted By sweety439
Well, can you add it to the list in post #87...

Well, can you add it to the list in post #87 (https://mersenneforum.org/showpost.php?p=533234&postcount=87)?
Forum: Lounge 2020-02-11, 04:15
Replies: 116
Sticky: Predict M52
Views: 7,581
Posted By sweety439
What are its prime factors?

What are its prime factors?
Forum: FactorDB 2020-02-11, 04:10
Replies: 440
Views: 30,380
Posted By sweety439
See...

See https://mersenneforum.org/showthread.php?t=10761, 2^16389+67607 have been certified as definitely prime, but see http://factordb.com/index.php?id=1100000000537223829, it is still "PRP" in...
Forum: sweety439 2020-02-11, 03:58
Replies: 159
Views: 7,909
Posted By sweety439
Well, can you give all data for (b-1)*b^n-1,...

Well, can you give all data for (b-1)*b^n-1, (b-1)*b^n+1, (b+1)*b^n-1, and (b+1)*b^n+1 for the b that you have searched? Besides, you seems have also searched the generalized repunit numbers...
Forum: Conjectures 'R Us 2020-02-11, 03:51
Replies: 32
Views: 1,283
Posted By sweety439
Can this problem be used for finding the smallest...

Can this problem be used for finding the smallest k (coprime to c) with covering set for the general case (k*b^n+c)/gcd(k+c,b-1)? For b>=2, c !=0, gcd(b,c)=1

Like this problem...
Showing results 1 to 25 of 1000

 
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