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Forum: sweety439 2020-10-20, 16:26
Replies: 41
Views: 4,058
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: 41
Views: 4,058
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: 214
Sticky: Prime-Wiki
Views: 19,436
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: 41
Views: 4,058
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: 41
Views: 4,058
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: 41
Views: 4,058
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: 88
Views: 85,646
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: 1,067
Views: 35,242
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: 58
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: 41
Views: 4,058
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
Forum: Lounge 2020-10-18, 10:25
Replies: 30
Views: 3,289
Posted By sweety439
There is a problem, the minimal set of the...

There is a problem, the minimal set of the strings for primes with at least two digits in base b:

https://primes.utm.edu/glossary/page.php?sort=MinimalPrime

In 1996, Jeffrey Shallit [Shallit96]...
Forum: And now for something completely different 2020-10-18, 09:25
Replies: 10
Views: 2,121
Posted By sweety439
https://oeis.org/A085398/b085398_2.txt

https://oeis.org/A085398/b085398_2.txt
Forum: Prime Wiki 2020-10-18, 09:00
Replies: 214
Sticky: Prime-Wiki
Views: 19,436
Posted By sweety439
80*81^5394+1, the second Williams MP prime base...

80*81^5394+1, the second Williams MP prime base 81 (the first is 80*81^1+1)

Done for 80*3^n+1 instead.
Forum: sweety439 2020-10-18, 07:20
Replies: 1,067
Views: 35,242
Posted By sweety439
Also all k-values such that numerator(k*b^n+-1)...

Also all k-values such that numerator(k*b^n+-1) (+ for Sierpinski, - for Riesel) divides (b-1)*b^r for some (positive or negative or 0) integer n and (positive or 0) integer r
Forum: sweety439 2020-10-18, 07:17
Replies: 1,067
Views: 35,242
Posted By sweety439
This also including all k-values such that k+-1...

This also including all k-values such that k+-1 (+ for Sierpinski, - for Riesel) divides (b-1)*b^r for some r
Forum: sweety439 2020-10-18, 02:54
Replies: 1,067
Views: 35,242
Posted By sweety439
No other (probable) primes found for R70 k = 376,...

No other (probable) primes found for R70 k = 376, 496, 811 up to n=22813
Forum: sweety439 2020-10-17, 09:38
Replies: 1
Views: 50
Posted By sweety439
M5 = 31, M7 = 127, W5 = 11, W7 = 43 It is...

M5 = 31, M7 = 127, W5 = 11, W7 = 43

It is known that MM5, MM7, WW5, WW7 are primes

However, MMM5 and WWW5 are both known to be composite

Two open problems: Is MMM7 prime? Is WWW7 prime?

I...
Forum: sweety439 2020-10-17, 06:55
Replies: 1
Views: 50
Posted By sweety439
Some notable smallest repunit/nexus prime

Let

a(b) = Smallest prime p such that the generalized repunit number (b^p-1)/(b-1) is prime
b(p) = Smallest base b such that the generalized repunit number (b^p-1)/(b-1) is prime
c(b) = Smallest...
Forum: Factoring 2020-10-16, 10:33
Replies: 3
Views: 234
Posted By sweety439
A general form is R(R(p,a),b), where a>=2, b>=2...

A general form is R(R(p,a),b), where a>=2, b>=2 are integers (define R(p,b) = (b^p-1)/(b-1) = generalized repunit base b with length p)

These are the smallest prime R(p,b) with prime p>2 in all...
Forum: sweety439 2020-10-16, 02:19
Replies: 1,067
Views: 35,242
Posted By sweety439
This is the sieve file for R70

This is the sieve file for R70
Forum: Cunningham Tables 2020-10-15, 22:11
Replies: 0
Views: 119
Posted By sweety439
Some special factorization status of generalized repunits

The generalized repunits (b^p-1)/(b-1) with a given factorization status

A = Semiprime and divisible by 2*p+1
B = Semiprime and the two prime factors are both large ((number of digits of the...
Forum: Prime Wiki 2020-10-15, 21:28
Replies: 214
Sticky: Prime-Wiki
Views: 19,436
Posted By sweety439
Recent status updating: 4*155^n+1 at 1.265M...

Recent status updating:

4*155^n+1 at 1.265M (https://mersenneforum.org/showpost.php?p=559194&postcount=843)

12*354^n+1 at 300K (https://mersenneforum.org/showpost.php?p=559825&postcount=2165)
...
Forum: sweety439 2020-10-13, 07:24
Replies: 1,067
Views: 35,242
Posted By sweety439
See...

See https://github.com/xayahrainie4793/Extended-Sierpinski-Riesel-conjectures/blob/master/Sierpinski%20CK%20for%20bases%20up%20to%202048.txt (Sierpinski) and...
Forum: sweety439 2020-10-13, 07:19
Replies: 1,067
Views: 35,242
Posted By sweety439
Now, the CK for all Sierpinski/Riesel bases <=...

Now, the CK for all Sierpinski/Riesel bases <= 1024 except SR156, SR280, SR876, SR910, R946, SR960, SR966 (which have too large upper bounds) are known!!!
Forum: sweety439 2020-10-13, 07:16
Replies: 1,067
Views: 35,242
Posted By sweety439
I skipped bases 876 and 966 because the covering...

I skipped bases 876 and 966 because the covering of the upper bound of these two bases (except the Riesel sides of 966) have a prime > 50000:

S876 and R876 have 59029
S966 has 71707

Like the...
Showing results 1 to 25 of 1000

 
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