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Forum: Math 2020-10-29, 18:20
Replies: 0
Views: 54
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: 1,074
Views: 36,613
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: 40,121
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: 1,074
Views: 36,613
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: 1,074
Views: 36,613
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: 1,074
Views: 36,613
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: 2,871
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: 48
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...
Forum: sweety439 2020-10-25, 19:43
Replies: 1,074
Views: 36,613
Posted By sweety439
R70 at n=37634, no new (probable) prime found

R70 at n=37634, no new (probable) prime found
Forum: sweety439 2020-10-25, 09:39
Replies: 2
Views: 96
Posted By sweety439
* If p is larger, then Rp(b) is harder to be...

* If p is larger, then Rp(b) is harder to be prime, the smallest base b such that Rp(b) is prime is about gamma*p (gamma is the Euler constant 0.577215664901...)

In general .... (let Rp(b) =...
Forum: And now for something completely different 2020-10-24, 16:28
Replies: 5
Views: 256
Posted By sweety439
Cullen-Williams primes and Woodall-Williams primes

The Cullen-Williams number base b is (b-1)*b^(b-1)+1, which is both Cullen number base b (n*b^n+1, some author requires n>=b-1, and for this number n is exactly b-1) and 2nd Williams number base b...
Forum: sweety439 2020-10-24, 16:20
Replies: 0
Views: 24
Posted By sweety439
47 & 383

They are not only two primes of the form 3*2^n-1, but also ....

* They are the first two non-Sophie-Germain primes (i.e. primes p such that 2*p+1 is not prime) of the form 3*2^n-1

* They are...
Forum: Number Theory Discussion Group 2020-10-24, 14:27
Replies: 27
Views: 847
Posted By sweety439
If Schinzel's hypothesis H...

If Schinzel's hypothesis H (https://en.wikipedia.org/wiki/Schinzel%27s_hypothesis_H) is true, then the second Hardy-Littlewood conjecture is false, since Schinzel's hypothesis H covers both...
Forum: Prime Wiki 2020-10-24, 14:19
Replies: 216
Sticky: Prime-Wiki
Views: 20,324
Posted By sweety439
9*830^n-1 at n=300K with no prime found...

9*830^n-1 at n=300K with no prime found (https://mersenneforum.org/showpost.php?p=560949&postcount=3743)
Forum: Prime Wiki 2020-10-23, 19:43
Replies: 216
Sticky: Prime-Wiki
Views: 20,324
Posted By sweety439
2*383^n+1 at n=1M with no prime found...

2*383^n+1 at n=1M with no prime found (https://mersenneforum.org/showpost.php?p=560850&postcount=2182)
Forum: Lounge 2020-10-23, 19:38
Replies: 44
Views: 3,651
Posted By sweety439
Dozenal is the best base!!! See page...

Dozenal is the best base!!! See page https://dozenal.fandom.com/wiki/10 and the links at the bottom of this page.
Forum: sweety439 2020-10-22, 14:59
Replies: 1,074
Views: 36,613
Posted By sweety439
For the Riesel bases 2<=b<=128 and b = 256, 512,...

For the Riesel bases 2<=b<=128 and b = 256, 512, 1024:

proven: 4, 5, 7 (with PRP), 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 23, 25, 26, 27, 29, 32, 34, 35, 37, 38, 39, 41, 44, 45, 47, 49,...
Forum: sweety439 2020-10-22, 14:48
Replies: 1,074
Views: 36,613
Posted By sweety439
For the Sierpinski bases 2<=b<=128 and b = 256,...

For the Sierpinski bases 2<=b<=128 and b = 256, 512, 1024:

proven: 4, 5, 7, 8, 9, 11, 13, 14, 16, 17, 19, 20, 21, 23, 27, 29, 34, 35, 39, 41, 43, 44, 45, 47, 49, 51, 54, 56, 57, 59, 61, 64, 65,...
Forum: Conjectures 'R Us 2020-10-22, 07:52
Replies: 17
Views: 1,857
Posted By sweety439
Is srsieve2 updated? If so, can you use it to...

Is srsieve2 updated? If so, can you use it to reserve the S3 problem in Sierpinski conjectures and proofs...
Forum: Cunningham Tables 2020-10-22, 06:36
Replies: 188
Views: 20,869
Posted By sweety439
Why 10^371+-1 are factored earlier than...

Why 10^371+-1 are factored earlier than 10^365+-1? eulerphi(371) = 312 > 288 = eulerphi(365)
Forum: sweety439 2020-10-21, 17:15
Replies: 43
Views: 4,328
Posted By sweety439
Although the test limit of all families in...

Although the test limit of all families in https://github.com/RaymondDevillers/primes are all 10K, but some families are in fact already tested to much higher....

Base 25:

EF{O}, 366*25^n-1:...
Forum: sweety439 2020-10-21, 16:06
Replies: 43
Views: 4,328
Posted By sweety439
Some minimal (probable) primes with bases...

Some minimal (probable) primes with bases 28<=b<=50 not shown in https://github.com/RaymondDevillers/primes: (and hence some unsolved families can be removed)

Base 37: (families FY{a} and R8{a}...
Forum: Five or Bust - The Dual Sierpinski Problem 2020-10-21, 15:37
Replies: 90
Views: 86,332
Posted By sweety439
2^unknown+79309 2^9+79817 2^42210+91549 (PRP)...

2^unknown+79309
2^9+79817
2^42210+91549 (PRP)
2^394+131179
2^21+152267
2^1032+156511
2^57+163187
2^1038+200749
2^44+202705
2^16+209611
Forum: sweety439 2020-10-20, 16:26
Replies: 43
Views: 4,328
Posted By sweety439
The "minimal prime problem" is solved only in...

The "minimal prime problem" is solved only in bases 2~16, 18, 20, 22~24, 30, 42, and maybe 60


b, length of largest minimal prime base b, number of minimal primes base b
2, 2, 2
3, 3, 3
4, 2,...
Forum: sweety439 2020-10-20, 15:49
Replies: 43
Views: 4,328
Posted By sweety439
Base 27: 8{0}9A: 5832*27^n+253 999{G}:...

Base 27:

8{0}9A: 5832*27^n+253
999{G}: (88577*27^n-8)/13
C{L}E: (8991*27^n-203)/26
E{I}F8: (139239*27^n-1192)/13
{F}9FM: (295245*27^n-113557)/26

Base 48:
Showing results 1 to 25 of 1000

 
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