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Forum: Homework Help 2022-05-25, 05:33
Replies: 3
Views: 317
Posted By sweety439
Because for all such primes p, 2^p-1 is divisible...

Because for all such primes p, 2^p-1 is divisible by 2*p+1, since 2*p+1 is == 7 mod 8, thus 2 is a quadratic residue (https://en.wikipedia.org/wiki/Quadratic_residue) mod 2*p+1, and...
Forum: FactorDB 2022-05-22, 23:13
Replies: 545
Views: 101,457
Posted By sweety439
P-1...

P-1 (https://en.wikipedia.org/wiki/Pollard%27s_p_%E2%88%92_1_algorithm) and P+1 (https://en.wikipedia.org/wiki/Williams%27s_p_%2B_1_algorithm) are "integer factoring" algorithm

N-1...
Forum: And now for something completely different 2022-05-22, 23:00
Replies: 129
Views: 32,933
Posted By sweety439
= = Are you sure that Primo can handle this large...

= = Are you sure that Primo can handle this large prime? Recently, the limit of Primo just extended from 40000 digits to 50000 digits, to make you can use Primo to prove R49081

Suggest you to...
Forum: sweety439 2022-05-22, 08:51
Replies: 417
Views: 33,595
Posted By sweety439
No, X1X1 (base 12) = 17545 (base 10), it is hard...

No, X1X1 (base 12) = 17545 (base 10), it is hard to find a positive multiple of 17545 which is palindromic number in base 12 (A029957 (https://oeis.org/A029957))
Forum: sweety439 2022-05-21, 23:14
Replies: 417
Views: 33,595
Posted By sweety439
Smallest k such that n*k is palindromic in...

Smallest k such that n*k is palindromic in dozenal (all n and k are written in dozenal)

Next term (n=X1X1) is very large, such number
Forum: sweety439 2022-05-21, 08:46
Replies: 35
Views: 1,810
Posted By sweety439
Can you prove the primality of these PRPs which...

Can you prove the primality of these PRPs which are in order to prove the Riesel...
Forum: sweety439 2022-05-21, 08:14
Replies: 35
Views: 1,810
Posted By sweety439
When will 8*13^32020+183...

When will 8*13^32020+183 (http://factordb.com/index.php?id=1100000000490878060) (the largest minimal prime (https://primes.utm.edu/glossary/xpage/MinimalPrime.html) in base 13, see...
Forum: FactorDB 2022-05-21, 07:34
Replies: 545
Views: 101,457
Posted By sweety439
Not delete the modulo operator (%), but just fix...

Not delete the modulo operator (%), but just fix this operator, also suggest lower case letters for variables, upper case letters for these functions: (delete these operators: "!!" = double factorial...
Forum: sweety439 2022-05-20, 22:20
Replies: 2
Views: 144
Posted By sweety439
A085398 (https://oeis.org/A085398)(n) is much...

A085398 (https://oeis.org/A085398)(n) is much large than all A085398 (https://oeis.org/A085398)(k) for all k<=n for:

* n=115, and if skip n=115, then n=119 (just larger than 115) is such n
*...
Forum: sweety439 2022-05-19, 20:13
Replies: 1,268
Views: 100,901
Posted By sweety439
All tested to n=6K, no prime or PRP found ...

All tested to n=6K, no prime or PRP found

bases released, reserve R181 (k=21)
Forum: sweety439 2022-05-19, 06:43
Replies: 5
Views: 2,470
Posted By sweety439
Mersenne exponents up to 127 ...

Mersenne exponents up to 127 Wagstaff exponents up to 127

2 (only Mersenne exists, since its corresponding Wagstaff number is not integer)
3, 5, 7
11 (11 is Wagstaff...
Forum: sweety439 2022-05-19, 06:35
Replies: 5
Views: 2,470
Posted By sweety439
MM2, MM3, MM5, MM7 are primes, and (conjectured)...

MM2, MM3, MM5, MM7 are primes, and (conjectured) MMp is composite if p>7.

WW3, WW5, WW7 are primes, and (conjectured) WWp is composite if p>7.

WM2, WM3, WM5, WM7 are primes (to satisfy the New...
Forum: sweety439 2022-05-19, 00:30
Replies: 1,268
Views: 100,901
Posted By sweety439
Take the following bases: R165 R178 (k=19)...

Take the following bases:

R165
R178 (k=19)
R186
Forum: sweety439 2022-05-17, 19:38
Replies: 417
Views: 33,595
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: 17,095
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: 83,370
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: 545
Views: 101,457
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: 4,685
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: 284
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: 1,009
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: 487
Views: 74,238
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: 2
Views: 144
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: 2
Views: 144
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: 487
Views: 74,238
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: 88,995
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
...
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