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Forum: Prime Wiki 2020-10-20, 14:11
Replies: 214
Sticky: Prime-Wiki
Views: 19,348
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: 39
Views: 3,997
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: 39
Views: 3,997
Posted By sweety439
Base 35: 6W{P}4: (288855*35^n-739)/34 ...

Base 35:

6W{P}4: (288855*35^n-739)/34
F8{0}F9: 652925*35^n+534
{Y}PO: 1225*35^n-326
FQ{F}I: (656215*35^n+87)/34
PX{0}ER: 1112300*35^n+517
Q{P}4: (31815*35^n-739)/34
RF{0}CPI:...
Forum: sweety439 2020-10-20, 12:35
Replies: 39
Views: 3,997
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: 87
Views: 85,513
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: 35,181
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: 50
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: 39
Views: 3,997
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: 3,271
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: 2,101
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: 19,348
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: 35,181
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: 35,181
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: 35,181
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: 48
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: 48
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: 232
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: 35,181
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: 105
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: 19,348
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: 35,181
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: 35,181
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: 35,181
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...
Forum: sweety439 2020-10-13, 07:12
Replies: 1,067
Views: 35,181
Posted By sweety439
The CK for S1020 is known to be 95696289 The CK...

The CK for S1020 is known to be 95696289
The CK for R1020 is known to be 94655888
Forum: Puzzles 2020-10-11, 20:25
Replies: 32
Views: 631
Posted By sweety439
They are all divisors of 360 (the number of...

They are all divisors of 360 (the number of degrees in a turn)
Showing results 1 to 25 of 1000

 
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