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Forum: sweety439 2020-10-31, 05:14
Replies: 1,082
Views: 36,923
Posted By sweety439
If this is generalized (half) Fermat number, but...

If this is generalized (half) Fermat number, but the equation 2^x == r (mod s) has no solution, then this k has no possible prime, thus excluded from the conjecture, like the k proven composite by...
Forum: sweety439 2020-10-31, 05:11
Replies: 1,082
Views: 36,923
Posted By sweety439
Let the divisor be d (i.e. d = gcd(k+-1,b-1) (+...

Let the divisor be d (i.e. d = gcd(k+-1,b-1) (+ for Sierpinski, - for Riesel))

* For the Riesel case, this is generalized repunit number to base d+1
* For the Sierpinski case, if d = 1, then this...
Forum: sweety439 2020-10-31, 05:00
Replies: 1,082
Views: 36,923
Posted By sweety439
Update files * Update newest status for R6...

Update files

* Update newest status for R6 k=1597
* Update newest status for R70
* Update newest status for S36 k=1814
* Fixed typo for S112 (the "Remaining k to find prime (n testing limit)"...
Forum: sweety439 2020-10-31, 04:57
Replies: 1,082
Views: 36,923
Posted By sweety439
S36 at n=92902, no (probable) prime found

S36 at n=92902, no (probable) prime found
Forum: sweety439 2020-10-31, 04:53
Replies: 1,082
Views: 36,923
Posted By sweety439
R70 at n=46072, no other (probable) prime found

R70 at n=46072, no other (probable) prime found
Forum: sweety439 2020-10-31, 03:45
Replies: 2
Views: 26
Posted By sweety439
GitHub Pages for the smallest n>=1 such that...

GitHub Pages for the smallest n>=1 such that (k*b^n+-1)/gcd(k+-1,b-1) created by me:

k<CK, b<=128 or 256, 512, 1024 (https://github.com/xayahrainie4793/Extended-Sierpinski-Riesel-conjectures)
...
Forum: sweety439 2020-10-31, 03:36
Replies: 2
Views: 26
Posted By sweety439
Link 1: * Smallest prime of the form...

Link 1:

* Smallest prime of the form k*b^n+-1 with n>=1 for bases 2<=b<=1030 and k<CK

Link 2:

* Primes of the form n*b^n-1 with n>=b-1 for bases 3<=b<=10000
* Primes of the form n*b^n+1...
Forum: sweety439 2020-10-31, 03:06
Replies: 2
Views: 26
Posted By sweety439
Link for primes collect

1. http://www.noprimeleftbehind.net/crus/
2. http://harvey563.tripod.com/
3. http://guenter.loeh.name/gc/status.html
4. http://www.fermatquotient.com/
5....
Forum: sweety439 2020-10-31, 00:54
Replies: 1,082
Views: 36,923
Posted By sweety439
For Riesel problem base b, k=1 proven composite...

For Riesel problem base b, k=1 proven composite by algebra factors if and only if b is perfect power (of the form m^r with r>1)

For Sierpinski problem base b, k=1 proven composite by algebra...
Forum: sweety439 2020-10-31, 00:24
Replies: 1,082
Views: 36,923
Posted By sweety439
reserving S36 k=1814 for n = 87.5K - 100K,...

reserving S36 k=1814 for n = 87.5K - 100K, currently at n=92334, no (probable) prime found
Forum: sweety439 2020-10-31, 00:22
Replies: 1,082
Views: 36,923
Posted By sweety439
These problems generalized the Sierpinski problem...

These problems generalized the Sierpinski problem (http://www.prothsearch.com/sierp.html) and the Riesel problem (http://www.prothsearch.com/rieselprob.html) to other bases (instead of only base 2),...
Forum: sweety439 2020-10-31, 00:09
Replies: 48
Views: 4,406
Posted By sweety439
The remain k < b (also including k > CK, if k <...

The remain k < b (also including k > CK, if k < b, e.g. 28*41^n+1 and 27*34^n-1) in CRUS corresponding to minimal primes to base b if and only if:

* In Sierpinski case, k is not prime (since it is...
Forum: sweety439 2020-10-31, 00:05
Replies: 48
Views: 4,406
Posted By sweety439
The GFN for these bases (always minimal primes): ...

The GFN for these bases (always minimal primes):

{38, 50, 62, 68, 86, 92, 98, 104, 122, 144, 168, 182, 186, 200, 202, 212, 214, 218, 244, 246, 252, 258, 286, 294, 298, 302, 304, 308, 322, 324,...
Forum: sweety439 2020-10-31, 00:02
Replies: 48
Views: 4,406
Posted By sweety439
There are no known generalized repunit (probable)...

There are no known generalized repunit (probable) primes in these bases <= 1024: (search limit: 100000)

{185, 269, 281, 380, 384, 385, 394, 452, 465, 511, 574, 601, 631, 632, 636, 711, 713, 759,...
Forum: sweety439 2020-10-30, 23:49
Replies: 228
Views: 13,999
Posted By sweety439
See...

See https://raw.githubusercontent.com/xayahrainie4793/Sierpinski-Riesel-for-fixed-k-and-variable-base/master/Riesel%20k1.txt for the status for the smallest generalized repunit prime (allow n=2) for...
Forum: sweety439 2020-10-30, 23:48
Replies: 48
Views: 4,406
Posted By sweety439
All smallest generalized repunit prime base b are...

All smallest generalized repunit prime base b are minimal prime base b, since they are of the form {1} in base b, for the smallest generalized repunit (probable) prime base b for b<=1024, see...
Forum: sweety439 2020-10-30, 23:05
Replies: 48
Views: 4,406
Posted By sweety439
Unsolved families which are CRUS...

Unsolved families which are CRUS Sierpinski/Riesel problems but with k's > CK:

Base 32:

G{0}1: 16*32^n+1
UG{0}1: 976*32^n+1

Base 33:

FFF{W}: 16846*33^n-1
Forum: Math 2020-10-29, 18:20
Replies: 0
Views: 61
Posted By sweety439
Two number theory questions

1. How many primes <= 12^n which is == k mod 12? For each values n = 10, 11, 12 and k = 1, 5, 7, 11

2. Find all Kaprekar's cycles for 9-digit to 12-digit dozenal numbers (a Kaprekar's cycle for...
Forum: sweety439 2020-10-29, 03:28
Replies: 1,082
Views: 36,923
Posted By sweety439
If k is rational power of base (b), then .......

If k is rational power of base (b), then .... (let k = b^(r/s) with gcd(r,s) = 1)

* For the Riesel case, this is generalized repunit number to base b^(1/s)
* For the Sierpinski case, if s is odd,...
Forum: Wagstaff PRP Search 2020-10-29, 02:19
Replies: 400
Views: 40,267
Posted By sweety439
Can you give a list for factorization for...

Can you give a list for factorization for Phi(n,2), like this factorization for Phi(n,2) for n<=1280 (https://oeis.org/A250197/a250197_2.txt), but for larger n, or the base 2 analog of...
Forum: sweety439 2020-10-29, 00:49
Replies: 1,082
Views: 36,923
Posted By sweety439
R70 at n=43008, one new (probable) prime found:...

R70 at n=43008, one new (probable) prime found: (376*70^42427-1)/3

Unfortunately, this does not help for the R70 problem, since k=376 already has the prime (376*70^6484-1)/3, and the only remain k...
Forum: sweety439 2020-10-28, 00:09
Replies: 1,082
Views: 36,923
Posted By sweety439
R43 at n=18122, no (probable) primes found ...

R43 at n=18122, no (probable) primes found

Unfortunately, srsieve cannot sieve R43, since k and b are both odd.
Forum: sweety439 2020-10-28, 00:07
Replies: 1,082
Views: 36,923
Posted By sweety439
R70 at n=41326, no other (probable) primes found

R70 at n=41326, no other (probable) primes found
Forum: Aliquot Sequences 2020-10-26, 13:54
Replies: 4
Views: 2,889
Posted By sweety439
The number 1578 merges to 56440, but it is not...

The number 1578 merges to 56440, but it is not known whether the sequence of 56440 (currently at 166 digits) also merges to 56440, thus it is not known whether 56440 is member of sociable number...
Forum: sweety439 2020-10-26, 12:17
Replies: 0
239
Views: 51
Posted By sweety439
239

Unlike the "very irregular prime" 311 -->

* 311 is Bernoulli irregular
* 311 is Euler irregular
* k*311+1 is composite for k = 2, 4, 8, 10, 14, 16
(these three properties make Fermat Last...
Showing results 1 to 25 of 1000

 
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