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Forum: sweety439 2022-07-05, 12:36
Replies: 355
Views: 45,601
Posted By sweety439
Some families cannot have covering sets (covering...

Some families cannot have covering sets (covering congruence, algebraic factorization, or combine of them) and thus there must be a prime of this form.

For the standard notation of family:...
Forum: sweety439 2022-07-02, 20:53
Replies: 355
Views: 45,601
Posted By sweety439
We have completely solved the "minimal prime >...

We have completely solved the "minimal prime > base problem" in bases 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 24

Also, we have completely solved the "minimal prime > base problem" in the...
Forum: sweety439 2022-07-01, 19:24
Replies: 355
Views: 45,601
Posted By sweety439
Some minimal primes (start with b+1) in...

Some minimal primes (start with b+1) in power-of-2 bases related to Sierpinski problem, Riesel problem, dual Sierpinski problem, dual Riesel problem (see https://oeis.org/A046067,...
Forum: sweety439 2022-07-01, 19:13
Replies: 355
Views: 45,601
Posted By sweety439
For a sub-problem of this problem, finding the...

For a sub-problem of this problem, finding the minimal (a,b,c) triple (i.e. there is no a' <= a, b' <= b, c' <= c, except the case a' = a and b' = b and c' = c) such that xxx...xxxyyy...yyyzzz...zzz...
Forum: sweety439 2022-07-01, 08:05
Replies: 0
Views: 40
Posted By sweety439
New Mixed Proth Theorem

See PrimeGrid New Sierpinski Problem (https://www.rieselprime.de/ziki/PrimeGrid_New_Sierpi%C5%84ski_Problem) and Mixed Sierpinski Theorem...
Forum: XYYXF Project 2022-06-30, 18:00
Replies: 570
Views: 126,031
Posted By sweety439
You have mtsieve...

You have mtsieve (https://sourceforge.net/projects/mtsieve/) + OpenPFGW (https://sourceforge.net/projects/openpfgw/), can I request you to build the list of generalized repunit primes?


ABC2...
Forum: And now for something completely different 2022-06-30, 17:35
Replies: 184
Views: 11,587
Posted By sweety439
For (10^1031-1)/9, N-1 can be easily >= 1/3...

For (10^1031-1)/9, N-1 can be easily >= 1/3 factored, and N-1 primality proving (https://primes.utm.edu/prove/prove3_1.html) can be used, I think 10^1000+453 (which is the next prime after 10^1000)...
Forum: XYYXF Project 2022-06-30, 17:24
Replies: 57
Views: 16,570
Posted By sweety439
I hope that factordb (http://factordb.com) can...

I hope that factordb (http://factordb.com) can add them.
Forum: XYYXF Project 2022-06-30, 17:08
Replies: 57
Views: 16,570
Posted By sweety439
A number pass a primality test (e.g. Fermat...

A number pass a primality test (e.g. Fermat primality test, strong primality test, Lucas strong primality test, strong Lucas primality test, …) need not be prime, for the smallest composites that...
Forum: Homework Help 2022-06-29, 18:11
Replies: 6
Views: 523
Posted By sweety439
7 and 13 are unique primes in base 2 7 is...

7 and 13 are unique primes in base 2

7 is the only prime with period length 3 in base 2, and 13 is the only prime with period length 12 in base 2

see factorization of Phi(n,2)...
Forum: sweety439 2022-06-29, 10:04
Replies: 43
Views: 7,224
Posted By sweety439
pdf file for broken link...

pdf file for broken link https://cbright.myweb.cs.uwindsor.ca/reports/cs662-problem12.pdf

from wayback machine:...
Forum: sweety439 2022-06-29, 10:03
Replies: 43
Views: 7,224
Posted By sweety439
pdf files related to minimal primes: Link 1:...

pdf files related to minimal primes:

Link 1: https://cs.uwaterloo.ca/~cbright/reports/mepn.pdf
Link 2: https://cs.uwaterloo.ca/~shallit/Papers/br10.pdf
Link 3:...
Forum: sweety439 2022-06-29, 10:00
Replies: 43
Views: 7,224
Posted By sweety439
Local copies of the pdf files: Original...

Local copies of the pdf files:

Original links of these pdf files:

Link 1: http://www.kurims.kyoto-u.ac.jp/EMIS/journals/INTEGERS/papers/i61/i61.pdf
Link 2:...
Forum: Factoring 2022-06-28, 17:32
Replies: 502
Views: 77,331
Posted By sweety439
What is the approximately equivalent for SNFS and...

What is the approximately equivalent for SNFS and GNFS? I guess that SNFS difficulty n is approximately equivalent to GNFS difficulty (2/3)*n, however, if my guess is true, then SNFS 210 is...
Forum: Miscellaneous Math 2022-06-27, 09:40
Replies: 32
Views: 824
Posted By sweety439
since they are two roots of x^2-x-1, their sum is...

since they are two roots of x^2-x-1, their sum is 1 and their product is -1 (in Z/nZ)

you can see all modulos < 1000 (https://mersenneforum.org/showpost.php?p=608246&postcount=5)

however, for...
Forum: Miscellaneous Math 2022-06-27, 09:36
Replies: 32
Views: 824
Posted By sweety439
Zp(i) is an quadratic extension field of the...

Zp(i) is an quadratic extension field of the field Zp if and only if p == 3 mod 4, if p == 1 mod 4, Zp(i) has zero divisors.
Forum: sweety439 2022-06-25, 14:20
Replies: 1,270
Views: 105,104
Posted By sweety439
R178 update k=19 has PRP at n=13655 k=4...

R178 update

k=19 has PRP at n=13655
k=4 remains at n=13K, continuing ....
Forum: Software 2022-06-24, 14:02
Replies: 5
Views: 224
Posted By sweety439
OK, I will run it myself.

OK, I will run it myself.
Forum: Software 2022-06-24, 13:52
Replies: 5
Views: 224
Posted By sweety439
So can you run the strong Lucas PRP test (with...

So can you run the strong Lucas PRP test (with parameters (P, Q) defined by Selfridge's Method A) for these seven numbers?
Forum: Software 2022-06-24, 13:08
Replies: 5
Views: 224
Posted By sweety439
Can PFGW run the strong Lucas primality test?

Can PFGW run the strong Lucas primality test, with parameters (P, Q) defined by Selfridge's Method A (see https://oeis.org/A217255 and http://ntheory.org/pseudoprimes.html)? I have used PFGW to...
Forum: sweety439 2022-06-24, 06:19
Replies: 355
Views: 45,601
Posted By sweety439
Now these minimal primes (start with b+1) in base...

Now these minimal primes (start with b+1) in base b have been proven primes: (only list the numbers > 10^1000)


b index of this minimal prime in base b base-b form of the minimal prime algebraic...
Forum: sweety439 2022-06-24, 06:09
Replies: 355
Views: 45,601
Posted By sweety439
This problem (the minimal prime (start with b+1)...

This problem (the minimal prime (start with b+1) problem) covers these problems:

* Find the smallest prime of the form (b^n-1)/(b-1) with n>=2 (or prove that such primes do not exist)
* Find the...
Forum: Miscellaneous Math 2022-06-24, 05:57
Replies: 32
Views: 824
Posted By sweety439
You want to use the series 1/0! + 1/1! + 1/2! +...

You want to use the series 1/0! + 1/1! + 1/2! + ... to calculated mod 11, but from 1/11!, the denominator is divisible by 11 and you will divide by zero.
Forum: And now for something completely different 2022-06-24, 05:53
Replies: 164
Views: 36,334
Posted By sweety439
The top Generalized Lucas Number...

The top Generalized Lucas Number (https://primes.utm.edu/top20/page.php?id=23) is U(24, - 25, 43201), which is equal to (25^43201+1)/26, but it is still "PRP" in factordb...
Forum: Factoring 2022-06-22, 14:17
Replies: 502
Views: 77,331
Posted By sweety439
The nontrivial parts are Phi(564,13) and...

The nontrivial parts are Phi(564,13) and Phi(576,13), where Phi is the cyclotomic polynomial (https://en.wikipedia.org/wiki/Cyclotomic_polynomial), thus the SNFS difficulty should be...
Showing results 1 to 25 of 1000

 
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