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Forum: sweety439 2022-01-28, 23:07
Replies: 285
Views: 30,292
Posted By sweety439
These (a*b^n+c)/gcd(a+c,b-1) (a>=1, b>=2, c != 0,...

These (a*b^n+c)/gcd(a+c,b-1) (a>=1, b>=2, c != 0, gcd(a,c) = 1, gcd(b,c) = 1) families are dual families (for the definition, see...
Forum: sweety439 2022-01-27, 15:31
Replies: 404
Views: 30,239
Posted By sweety439
upload data files and program files

upload data files and program files
Forum: sweety439 2022-01-26, 23:46
Replies: 1,257
Views: 88,496
Posted By sweety439
R243 k=81 remains, such prime must be generalized...

R243 k=81 remains, such prime must be generalized repunit prime base 3, recently two generalized repunit primes base 3 are found: (3^2704981-1)/2 and (3^3598867-1)/2 (see A028491...
Forum: sweety439 2022-01-26, 23:43
Replies: 15
Views: 6,814
Posted By sweety439
Some examples (a*b^n+c)/gcd(a+c,b-1) (a>=1, b>=2,...

Some examples (a*b^n+c)/gcd(a+c,b-1) (a>=1, b>=2, c != 0, gcd(a,c) = 1, gcd(b,c) = 10 of dual families:

b^n+1 (self dual) (b == 0 mod 2)
(b^n-1)/(b-1) (self dual)
(b^n+1)/2 (self dual) (b == 1...
Forum: sweety439 2022-01-25, 00:24
Replies: 285
Views: 30,292
Posted By sweety439
A conjecture between this minimal prime problem...

A conjecture between this minimal prime problem (i.e. start with b+1) and the original minimal prime problem (https://cs.uwaterloo.ca/~cbright/reports/mepn.pdf) (i.e. p > b is not required): In all...
Forum: sweety439 2022-01-24, 13:06
Replies: 285
Views: 30,292
Posted By sweety439
Thus, the total proof of base 10 includes these...

Thus, the total proof of base 10 includes these proofs:

* Prove that all of 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409,...
Forum: sweety439 2022-01-22, 18:56
Replies: 404
Views: 30,239
Posted By sweety439
Numbers n such that Phi(n,a,b) =...

Numbers n such that Phi(n,a,b) = b^eulerphi(n)*Phi(n,a/b) is prime, "*" for Phi(n,a,b)/gcd(Phi(n,a,b),n) is prime

reference: https://oeis.org/A250201
Forum: sweety439 2022-01-22, 10:47
Replies: 18
Views: 1,072
Posted By sweety439
Related conjectures: 11 is the only...

Related conjectures:

11 is the only non-generalized pentagonal number which cannot be written as sum of a prime and a positive generalized pentagonal number.

besides 1 and 3, 79 is the only odd...
Forum: sweety439 2022-01-21, 21:51
Replies: 18
Views: 1,072
Posted By sweety439
The numbers in A347567: {1, 3, 4, 6, 10, 17,...

The numbers in A347567:

{1, 3, 4, 6, 10, 17, 20, 26, 62, 68, 74, 116, 122, 137, 170, 182, 227, 254, 260, 428, 452, 740, 758, 878, 977, 1052, 1142, 1187, 1412, 1460, 1493, 1542, 1658, 1982, 2510,...
Forum: sweety439 2022-01-21, 21:32
Replies: 18
Views: 1,072
Posted By sweety439
For A347567, 2*square+p, where p is either odd...

For A347567, 2*square+p, where p is either odd prime or twice an odd prime, the set is:

{1, 3, 4, 6, 10, 17, 20, 26, 62, 68, 74, 116, 122, 137, 170, 182, 227, 254, 260, 428, 452, 740, 758, 878,...
Forum: sweety439 2022-01-21, 15:52
Replies: 285
Views: 30,292
Posted By sweety439
the last (i.e. Proving that all primes > 10...

the last (i.e. Proving that all primes > 10 contain at least one element in {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409,...
Forum: sweety439 2022-01-21, 15:44
Replies: 285
Views: 30,292
Posted By sweety439
zipped file for the minimal primes (start with...

zipped file for the minimal primes (start with b+1) in bases 17<=b<=36
Forum: sweety439 2022-01-20, 22:18
Replies: 18
Views: 1,072
Posted By sweety439
The conjecture 2 in post #1...

The conjecture 2 in post #1 (https://mersenneforum.org/showpost.php?p=592782&postcount=1) (i.e. A347568 (https://oeis.org/A347568) is full with 8 terms: {1, 3, 4, 10, 14, 122, 422, 432}):

Zhi-Wei...
Forum: sweety439 2022-01-20, 10:26
Replies: 404
Views: 30,239
Posted By sweety439
https://sites.google.com/view/williams-primes ...

https://sites.google.com/view/williams-primes

https://sites.google.com/view/nexus-primes
Forum: Prime Wiki 2022-01-20, 10:21
Replies: 45
Views: 3,659
Posted By sweety439
Now I search the Williams primes...

Now I search the Williams primes (https://www.rieselprime.de/ziki/Williams_prime) (of all 8 kinds) to n=5000 (now done to base 45) and create a website (https://sites.google.com/view/williams-primes)...
Forum: sweety439 2022-01-18, 10:11
Replies: 1,257
Views: 88,496
Posted By sweety439
Sierpinski conjectures (k*b^n+1)/gcd(k-1,b+1):...

Sierpinski conjectures (k*b^n+1)/gcd(k-1,b+1): [b,k]

(GFN and half GFN not counted)

[2,21181]

b=2, k<=21180

[3,1187]
Forum: sweety439 2022-01-18, 10:01
Replies: 1,257
Views: 88,496
Posted By sweety439
Riesel conjectures (k*b^n-1)/gcd(k-1,b-1): [b,k] ...

Riesel conjectures (k*b^n-1)/gcd(k-1,b-1): [b,k]

[2,23669]

b=2, k<=23668

[3,1613]

b<=4, k<=1612
Forum: Aliquot Sequences 2022-01-18, 09:53
Replies: 1,029
Views: 125,318
Posted By sweety439
Is this a new record for the largest number in a...

Is this a new record for the largest number in a terminate aliquot sequence? (the largest number in this sequence is index 2789 (http://factordb.com/index.php?id=1100000001517282545))
Forum: sweety439 2022-01-17, 06:17
Replies: 285
Views: 30,292
Posted By sweety439
find the set of the minimal primes (start with...

find the set of the minimal primes (start with b+1) base b for various bases b (2<=b<=36) is the target of the project in this thread.

minimal prime (start with b+1) base b is always minimal prime...
Forum: sweety439 2022-01-16, 17:13
Replies: 0
Views: 38
Posted By sweety439
Off-topic

Like Cunningham table (https://homes.cerias.purdue.edu/~ssw/cun/index.html) to various bases, is there any interest to factor the numbers similar to Fibonacci numbers A000045...
Forum: sweety439 2022-01-16, 17:05
Replies: 18
Views: 1,072
Posted By sweety439
There are complement of A065377...

There are complement of A065377 (https://oeis.org/A065377) and A065397 (https://oeis.org/A065397) of the primes A000040 (https://oeis.org/A000040) in OEIS: A065376 (https://oeis.org/A065376) and...
Forum: sweety439 2022-01-16, 16:55
Replies: 18
Views: 1,072
Posted By sweety439
Compare with the numbers with only one way to...

Compare with the numbers with only one way to write as:

"twice a positive square number" + "odd prime or twice an odd prime"

or

"twice a positive triangular number" + "odd prime or twice an...
Forum: sweety439 2022-01-16, 11:48
Replies: 18
Views: 1,072
Posted By sweety439
Related research: perfect power...

Related research: perfect power (https://oeis.org/A001597) (0 and 1 are not counted as perfect power) + prime (the even prime 2 is allowed)

OEIS sequences for this: A119748...
Forum: sweety439 2022-01-15, 07:11
Replies: 285
Views: 30,292
Posted By sweety439
Conjecture: There is no base b such that the...

Conjecture: There is no base b such that the largest minimal prime (start with b+1) and the second-largest minimal prime (start with b+1) have the same number of digits in base b, note that in the...
Forum: sweety439 2022-01-15, 06:55
Replies: 2
Views: 50
Posted By sweety439
b-file (or a-file): (rows m = 1 to m = 12 of...

b-file (or a-file):

(rows m = 1 to m = 12 of the triangle (indices i = 1 to i = 78), flattened, row m = 1 has index i = 1, row m = 2 has index i = {2,3}, row m = 3 has index i = {4,5,6}, row m = 4...
Showing results 1 to 25 of 1000

 
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