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Forum: sweety439 2022-07-01, 08:05
Replies: 0
Views: 11
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: 536
Views: 124,953
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: 179
Views: 11,034
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: 16,468
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: 16,468
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: 441
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: 7,196
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: 7,196
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: 7,196
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: 76,977
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: 28
Views: 664
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: 28
Views: 664
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: 104,646
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: 211
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: 211
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: 211
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: 351
Views: 45,234
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: 351
Views: 45,234
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: 28
Views: 664
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: 36,175
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: 76,977
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...
Forum: sweety439 2022-06-22, 11:13
Replies: 0
Views: 75
Posted By sweety439
Smallest GFN divisors

Smallest k such that k*2^(n+1)+1 is prime and divides GFN(b,n) = b^(2^n)+1 (such prime factors must be == 1 mod 2^(n+1)), for 2<=b<=40, 1<=n<=40

search limit of k: 2^24


b: n = 1 to 40
2: 1,...
Forum: Factoring 2022-06-22, 08:57
Replies: 502
Views: 76,977
Posted By sweety439
Yes, I copy-and-paste, but copied the wrong...

Yes, I copy-and-paste, but copied the wrong texts.

So how to use SNFS or GNFS to factor 13^282+1 and 13^288+1? They seems to have low difficulty.
Forum: Factoring 2022-06-22, 06:53
Replies: 502
Views: 76,977
Posted By sweety439
How to use SNFS or GNFS to factor the composite...

How to use SNFS or GNFS to factor the composite cofactors of 13^282+1 and 13^288+1 (they only have 147 digits and 13^288+1, respectively, also their SNFS difficulty are low)
Forum: sweety439 2022-06-22, 04:14
Replies: 2
Views: 146
Posted By sweety439
Properties of the dozenal system

All squares end with square digits (i.e. end with 0, 1, 4 or 9), if n is divisible by both 2 and 3, then n2 ends with 0, if n is not divisible by 2 or 3, then n2 ends with 1, if n is divisible by 2...
Showing results 1 to 25 of 1000

 
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