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Forum: sweety439 2020-10-25, 19:43
Replies: 1,070
Views: 35,846
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: 83
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: 3
Views: 119
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: 20
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: 19
Views: 499
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: 19,872
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: 19,872
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: 3,535
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: 1,070
Views: 35,846
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: 1,070
Views: 35,846
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: 1,723
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: 20,359
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: 4,218
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: 4,218
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: 86,012
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: 4,218
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: 4,218
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:
Forum: Prime Wiki 2020-10-20, 14:11
Replies: 216
Sticky: Prime-Wiki
Views: 19,872
Posted By sweety439
4*230^n+1 at n=1M with no prime found...

4*230^n+1 at n=1M with no prime found (https://mersenneforum.org/showpost.php?p=560395&postcount=852)
Forum: sweety439 2020-10-20, 13:31
Replies: 43
Views: 4,218
Posted By sweety439
Base 25: F{O}KO: 9375*25^n+524 FO{K}O:...

Base 25:

F{O}KO: 9375*25^n+524
FO{K}O: (56375*25^n+19)/6
LO{L}8: (109975*25^n-111)/8 [need not to be searched if a smaller prime for the "O{L}8: (4975*25^n-111)/8" family were found]
M{1}F1:...
Forum: sweety439 2020-10-20, 12:48
Replies: 43
Views: 4,218
Posted By sweety439
Base 35: 6W{P}4: (288855*35^n-739)/34 [need...

Base 35:

6W{P}4: (288855*35^n-739)/34 [need not to be searched if a smaller prime for the "W{P}4: (38955*35^n-739)/34" family were found]
F8{0}F9: 652925*35^n+534
{Y}PO: 1225*35^n-326
FQ{F}I:...
Forum: sweety439 2020-10-20, 12:35
Replies: 43
Views: 4,218
Posted By sweety439
Base 31: ILE{L}: (179637*31^n-7)/10 [need...

Base 31:

ILE{L}: (179637*31^n-7)/10 [need not to be searched if a smaller prime for the "IE{L}: (5727*31^n-7)/10" family were found]
L{F}G: (1333*31^n+1)/2 [need not to be searched if a smaller...
Forum: Five or Bust - The Dual Sierpinski Problem 2020-10-20, 12:09
Replies: 90
Views: 86,012
Posted By sweety439
For the dual Sierpinski problem for...

For the dual Sierpinski problem for 78557<k<271129, I found that 2^42210+91549 is (probable) prime, but I cannot find a (probable) prime for 2^n+79309, can someone find it?
Forum: sweety439 2020-10-19, 15:47
Replies: 1,070
Views: 35,846
Posted By sweety439
At n=26544, found a new (probable) prime:...

At n=26544, found a new (probable) prime: (376*70^24952-1)/3
Forum: sweety439 2020-10-19, 15:45
Replies: 2
757
Views: 68
Posted By sweety439
757

757 is irregular prime
757 is de Polignac number (cannot be written as 2^n+p with prime p)
757 is the smallest prime p such that 1/p has period length 3^3 (in decimal)
The smallest n such that...
Forum: sweety439 2020-10-18, 13:39
Replies: 43
Views: 4,218
Posted By sweety439
Unsolved families: Base 17: F1{9}:...

Unsolved families:

Base 17:

F1{9}: (4105*17^n-9)/16

Base 19:

EE1{6}: (15964*19^n-1)/3
Showing results 1 to 25 of 1000

 
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