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Forum: sweety439 2020-07-15, 23:27
Replies: 906
Views: 26,148
Posted By sweety439
Store the files for R42 k=3 and k=14 (3*14=42,...

Store the files for R42 k=3 and k=14 (3*14=42, thus they are duals)

these solved R1764 k=14, k=126=3*42, k=588=14*42, but k=3 is still unsloved
Forum: Miscellaneous Math 2020-07-15, 22:52
Replies: 15
Views: 212
Posted By sweety439
3061 is an interesting k, this k is a potential...

3061 is an interesting k, this k is a potential SierpiƄski number ((k*b^n+1)/gcd(k+1,b-1) is not prime for small n (usually n<=10K)) to both base 2 and base 3, the smallest n for k=3061 b=2 is 33288,...
Forum: Lounge 2020-07-15, 22:41
Replies: 22
Views: 1,729
Posted By sweety439
You can use ASCII character n+32 to represent n...

You can use ASCII character n+32 to represent n for base 95, see http://www.icerealm.org/FTR/?s=docs&p=base95
Forum: Miscellaneous Math 2020-07-15, 22:40
Replies: 15
Views: 212
Posted By sweety439
By Chinese remainder theorem, such k always...

By Chinese remainder theorem, such k always exists, but unknown.

For base 3, do you allow odd k or only allow even k? For odd k, you should use the formula (k*3^n+1)/2 instead of k*3^n+1 because...
Forum: Miscellaneous Math 2020-07-15, 21:20
Replies: 15
Views: 212
Posted By sweety439
The solutions are already found for bases <= 2048...

The solutions are already found for bases <= 2048

(this is for k*b^n+-1 with gcd(k+-1,b-1) = 1 (+ for Sierpinski, - for Riesel), while the files in post #6...
Forum: sweety439 2020-07-15, 21:15
Replies: 906
Views: 26,148
Posted By sweety439
(Probable) primes with n>=1000 and smaller (b,k):...

(Probable) primes with n>=1000 and smaller (b,k):

Sierpinski:

b=2: (see http://www.prothsearch.com/sierp.html)

b=3:

k=41, n=4892 (k=123, n=4891, k=369, n=4890, k=1107, n=4889)
k=523,...
Forum: Miscellaneous Math 2020-07-15, 17:09
Replies: 15
Views: 212
Posted By sweety439
Some of more complex examples of the k's making a...

Some of more complex examples of the k's making a full covering set with all or partial algebraic factors:

25*12^n-1
27*12^n-1
64*12^n-1
(81*17^n-1)/16
144*28^n-1
(289*28^n-1)/9...
Forum: Miscellaneous Math 2020-07-15, 16:58
Replies: 15
Views: 212
Posted By sweety439
I only think the k's having a single set of fixed...

I only think the k's having a single set of fixed numeric factors as Sierpinski/Riesel numbers, thus I do not think these k's for (1*4^n-1)/3, (1*9^n-1)/8, 4*9^n-1, (4*19^n-1)/3, 4*24^n-1,...
Forum: Conjectures 'R Us 2020-07-15, 05:21
Replies: 3,686
Views: 216,323
Posted By sweety439
The CRUS page does not show the prime...

The CRUS page does not show the prime 12*600^11241+1, see post https://mersenneforum.org/showpost.php?p=518762&postcount=93
Forum: sweety439 2020-07-15, 00:25
Replies: 906
Views: 26,148
Posted By sweety439
These ranges are completed: "[]" for the...

These ranges are completed: "[]" for the remaining (b,k) pair such that no smaller k for this b, no smaller b for this k, no smaller b and smaller k, are remaining.

(b>=2, k>=1)

Sierpinski:
...
Forum: FactorDB 2020-07-14, 22:28
Replies: 444
Views: 34,619
Posted By sweety439
There are two ID's for the Fermat number F26: ...

There are two ID's for the Fermat number F26:

1100000000785073549 (http://factordb.com/index.php?id=1100000000785073549)

1100000001405019228...
Forum: PrimeNet 2020-07-14, 22:25
Replies: 34
Views: 2,932
Posted By sweety439
Every odd prime p must divide Phi_d(2) for a...

Every odd prime p must divide Phi_d(2) for a number d dividing p-1, thus, for p=367, 367 must divide Phi_d(2) for one of these numbers (divisors of 366): 1, 2, 3, 6, 61, 122, 183, 366
Forum: PrimeNet 2020-07-14, 22:16
Replies: 34
Views: 2,932
Posted By sweety439
(2^M127+1)/3 is divisible by...

(2^M127+1)/3 is divisible by 886407410000361345663448535540258622490179142922169401, thus not prime.

Therefore, if MM127 is prime, then the New Mersenne Conjecture is false (failed at n=M127).
...
Forum: PrimeNet 2020-07-14, 19:43
Replies: 34
Views: 2,932
Posted By sweety439
Conjectures: * The largest double Mersenne...

Conjectures:

* The largest double Mersenne prime is 2^127-1

* The largest Wagstaff Mersenne prime is (2^127+1)/3

* The largest Mersenne Wagstaff prime is 2^3-1

* The largest double...
Forum: PrimeNet 2020-07-14, 19:38
Replies: 34
Views: 2,932
Posted By sweety439
The Wagstaff Mersenne number...

The Wagstaff Mersenne number (2170141183460469231731687303715884105727+1)/3 has a factor: 886407410000361345663448535540258622490179142922169401

See...
Forum: Miscellaneous Math 2020-07-14, 19:33
Replies: 8
Views: 541
Posted By sweety439
The general number is Phi_n(2), where Phi is the...

The general number is Phi_n(2), where Phi is the cyclotomic polynomial, which may be prime or composite, the value of Phi_n(2) for n = 1, 2, 3, ... are 1, 3, 7, 5, 31, 3, 127, 17, 73, 11, 2047, 13,...
Forum: Miscellaneous Math 2020-07-14, 17:50
Replies: 15
Views: 212
Posted By sweety439
See post...

See post https://mersenneforum.org/showpost.php?p=549717&postcount=853
Forum: Miscellaneous Math 2020-07-14, 16:01
Replies: 15
Views: 212
Posted By sweety439
Conjecture 1 (the strong Sierpinski conjecture):...

Conjecture 1 (the strong Sierpinski conjecture): For b>=2, k>=1, if there is an n such that:

(1) k*b^n is neither a perfect odd power (i.e. k*b^n is not of the form m^r with odd r>1) nor of the...
Forum: Miscellaneous Math 2020-07-14, 15:56
Replies: 15
Views: 212
Posted By sweety439
This is the conjectured smallest...

This is the conjectured smallest Sierpinski/Riesel number in new definition to base b for 2<=b<=2048, "NA" if the smallest such number is > 10^6

Original definition: k's such that k*b^n+-1 (+ for...
Forum: Miscellaneous Math 2020-07-14, 15:30
Replies: 15
Views: 212
Posted By sweety439
I also have another definition of...

I also have another definition of Sierpinski/Riesel numbers extended to the k such that gcd(k+-1,b-1) (+ for Sierpinski, - for Riesel) is not 1, since k*b^n+-1 is always divisible by gcd(k+-1,b-1),...
Forum: Miscellaneous Math 2020-07-14, 15:22
Replies: 15
Views: 212
Posted By sweety439
Also, k's making a full covering set with all or...

Also, k's making a full covering set with all or partial algebraic factors are not consider as Sierpinski/Riesel numbers, since they do not have a single set of fixed numeric factors. e.g. 8 is not...
Forum: sweety439 2020-07-14, 12:14
Replies: 906
Views: 26,148
Posted By sweety439
Update newest status of Sierpinski problems...

Update newest status of Sierpinski problems (https://docs.google.com/document/d/e/2PACX-1vTsmy_HaE-GxLL6ICfbvUNr9iXdkgQfuVYpPkFPFUjPerzPglR11zObhWRdG7YlLd5judUF8OgSUVsS/pub)

S81 has only 7 k remain
Forum: sweety439 2020-07-14, 11:57
Replies: 906
Views: 26,148
Posted By sweety439
There are two other errors (for k=317 and 389):...

There are two other errors (for k=317 and 389): (317*81^518+1)/gcd(317+1,81-1) and (389*81^871+1)/gcd(389+1,81-1) are primes

Re-update the zip file
Forum: sweety439 2020-07-14, 11:51
Replies: 906
Views: 26,148
Posted By sweety439
Found an error of S81:...

Found an error of S81: (34*81^734+1)/gcd(34+1,81-1) is prime

Double checking S81....
Forum: sweety439 2020-07-12, 19:47
Replies: 906
Views: 26,148
Posted By sweety439
These bases b have many small Sierpinski/Riesel...

These bases b have many small Sierpinski/Riesel numbers k:


base Sierpinski numbers k Riesel numbers k
5 == 7, 11 mod 24 == 13, 17 mod 24...
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