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Forum: sweety439 2022-05-17, 19:38
Replies: 413
Views: 33,314
Posted By sweety439
OEIS sequences of smallest Proth primes...

OEIS sequences of smallest Proth primes (k*b^n+1), smallest Riesel primes (k*b^n-1), smallest dual Proth primes (b^n+k), smallest dual Riesel primes (b^n-k):


k smallest Proth primes...
Forum: sweety439 2022-05-17, 19:28
Replies: 74
Views: 17,012
Posted By sweety439
The record values: Base 2: Appending...

The record values:

Base 2:

Appending 1's:

1 (1)
4 (2)
12 (3)
13 (4)
Forum: FactorDB 2022-05-16, 21:54
Replies: 440
Views: 83,114
Posted By sweety439
The generalized repunit probable prime,...

The generalized repunit probable prime, R2731(685) (http://factordb.com/index.php?id=1100000000491221598), N-1 (http://factordb.com/index.php?id=1100000000491221888) has 31.345% factored, all...
Forum: FactorDB 2022-05-15, 14:14
Replies: 541
Views: 100,718
Posted By sweety439
There were many small composites < 10^18...

There were many small composites < 10^18 (https://archive.ph/9D4aU) (from a bug) in Oct 2021, and all of them had been deleted, but there were also many small primes < 10^18...
Forum: Dobri 2022-05-14, 16:06
Replies: 53
Views: 4,423
Posted By sweety439
OEIS sequences references of your problem: ...

OEIS sequences references of your problem:

https://oeis.org/A007350
https://oeis.org/A007352
https://oeis.org/A199547
https://oeis.org/A306891
https://oeis.org/A038698...
Forum: sweety439 2022-05-14, 13:36
Replies: 3
Views: 269
Posted By sweety439
We use "infinity" instead of "0" or "-1" because...

We use "infinity" instead of "0" or "-1" because ...

* infinity is > any finite number, this is more convenient (e.g. the smallest n such that (k^n-1)/(k-1) is prime, for k = 185, (k^n-1)/(k-1)...
Forum: sweety439 2022-05-13, 21:23
Replies: 13
Views: 949
Posted By sweety439
First holes: b=2~401...

First holes:

b=2~401 (http://myfactorcollection.mooo.com:8090/cgi-bin/showFH?FBase=2&TBase=401&c0=)
Forum: Factoring 2022-05-13, 20:14
Replies: 484
Views: 73,743
Posted By sweety439
Indeed, when I try to use N-1 proof...

Indeed, when I try to use N-1 proof (https://primes.utm.edu/prove/prove3_1.html) or N+1 proof (https://primes.utm.edu/prove/prove3_2.html) for the generalized repunit primes...
Forum: sweety439 2022-05-12, 23:20
Replies: 1
Views: 83
Posted By sweety439
Strictly generalized repunit primes

Like the sense ...

Generalized Cullen primes base b: primes of the form n*b^n+1 (https://oeis.org/A240234)
Generalized Woodall primes base b: primes of the form n*b^n-1 (https://oeis.org/A240235)...
Forum: sweety439 2022-05-12, 22:58
Replies: 1
Views: 83
Posted By sweety439
Curious of generalized repunit primes

Mersenne conjectured that for primes p <= 257, 2^p-1 is prime if and only if p = {2, 3, 5, 7, 13, 17, 19, 31, 67, 127, 257}, but this is not true, the correct one is: for primes p <= 257, 2^p-1 is...
Forum: Factoring 2022-05-12, 22:05
Replies: 484
Views: 73,743
Posted By sweety439
89^145-1...

89^145-1 (http://factordb.com/index.php?id=1100000000008232208) is already fully factored.
Forum: Factoring 2022-05-12, 22:04
Replies: 86
Views: 88,812
Posted By sweety439
https://www.numberempire.com/numberfactorizer.php...

https://www.numberempire.com/numberfactorizer.php

https://www.alpertron.com.ar/ECM.HTM

http://www.javascripter.net/math/calculators/primefactorscalculator.htm
...
Forum: sweety439 2022-05-12, 12:59
Replies: 329
Views: 40,708
Posted By sweety439
The minimal prime in family 1{z} in base b...

The minimal prime in family 1{z} in base b (always minimal prime (start with b+1) base b) has length 2 if and only if the minimal prime in family 1{0}z in base b (always minimal prime (start with...
Forum: sweety439 2022-05-12, 12:59
Replies: 329
Views: 40,708
Posted By sweety439
The possible length of a prime in the families...

The possible length of a prime in the families (in any base b) are: (the length is possible if and only if the corresponding polynomial of the base b satisfies the condition in Bunyakovsky conjecture...
Forum: sweety439 2022-05-08, 14:14
Replies: 329
Views: 40,708
Posted By sweety439
bases 9, 10, 12

bases 9, 10, 12
Forum: sweety439 2022-05-07, 12:39
Replies: 329
Views: 40,708
Posted By sweety439
upload the base 9 file.

upload the base 9 file.
Forum: sweety439 2022-05-07, 10:56
Replies: 4
Views: 136
Posted By sweety439
Well, can someone update the Windows version of...

Well, can someone update the Windows version of Primo?
Forum: Cunningham Tables 2022-05-07, 10:55
Replies: 56
Sticky: 7- table
Views: 36,110
Posted By sweety439
7,379- was already done in December 2021

7,379- was already done in December 2021
Forum: sweety439 2022-05-07, 08:51
Replies: 25
Views: 1,462
Posted By sweety439
Predict the smallest integer n such that 67607*2^n+1 is prime

Sierpinski conjectured that 78557 is the smallest odd k such that k*2^n+1 is composite for all integer n (for k = 78557, k*2^n+1 must be divisible by at least one of {3, 5, 7, 13, 19, 37, 73}, thus...
Forum: sweety439 2022-05-07, 08:44
Replies: 4
Views: 136
Posted By sweety439
Minus Yet another trivial "do this"

There is a much smaller interesting number: (64*10^10906+53)/9 (http://factordb.com/index.php?id=1000000000008860930), with "only" 10907 digits, which is 7111...1117 with 10905 1's, and is the...
Forum: Miscellaneous Math 2022-05-06, 12:45
Replies: 29
Views: 1,005
Posted By sweety439
Well, my article...

Well, my article (https://docs.google.com/document/d/e/2PACX-1vQct6Hx-IkJd5-iIuDuOKkKdw2teGmmHW-P75MPaxqBXB37u0odFBml5rx0PoLa0odTyuW67N_vn96J/pub) has many examples of algebraic factorization and...
Forum: Miscellaneous Math 2022-05-06, 06:48
Replies: 29
Views: 1,005
Posted By sweety439
Only trial division...

Only trial division (https://primes.utm.edu/glossary/xpage/TrialDivision.html) can be used (if the number has small prime factors, say < 2^32), e.g. large Fermat numbers...
Forum: Miscellaneous Math 2022-05-06, 02:33
Replies: 29
Views: 1,005
Posted By sweety439
Can Prime95 do a PRP test on general case...

Can Prime95 do a PRP test on general case (k*b^n+c)/gcd(k+c,b-1) (see my minimal prime problem...
Forum: sweety439 2022-05-05, 02:42
Replies: 1,266
Views: 99,616
Posted By sweety439
R515 has CK = 5 (for all bases b == 14 mod 15, 4...

R515 has CK = 5 (for all bases b == 14 mod 15, 4 is both Sierpinski and Riesel, and for all bases b == 11 mod 12, 5 is both Sierpinski and Riesel)

thus this base is trivial, only k = 1 through k =...
Forum: sweety439 2022-05-05, 02:37
Replies: 1,266
Views: 99,616
Posted By sweety439
R792 is also an interesting base, as there are...

R792 is also an interesting base, as there are many k's with algebraic factorization (combine of difference of squares and one-covering)

CK = 365, covering set = {13, 61}

tested to n=2000

...
Showing results 1 to 25 of 1000

 
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