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Forum: Homework Help 2022-06-29, 18:11
Replies: 6
Views: 397
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: 7,188
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: 7,188
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: 7,188
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: 76,888
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: 657
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: 657
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: 104,564
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: 207
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: 207
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: 207
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: 45,141
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: 45,141
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: 657
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: 36,104
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: 76,888
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: 76,888
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: 76,888
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: 144
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...
Forum: sweety439 2022-06-22, 03:53
Replies: 2
Views: 144
Posted By sweety439
properties of the number 10 (all written in dozenal)

An interesting thing is 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + X + E + 10 + ... = −1/10 = −0.1, i.e.
$ \sum_{k=1}^{\infty}(k)=-\frac{1}{10}=-0.1 $ (this number is
$ \zeta(-1) $ , which equals the...
Forum: Miscellaneous Math 2022-06-22, 03:45
Replies: 10
Views: 349
Posted By sweety439
Your perfect number is even or odd? All even...

Your perfect number is even or odd?

All even perfect numbers must be of the form 2^(p-1)*(2^p-1) with 2^p-1 prime.
Forum: sweety439 2022-06-22, 03:08
Replies: 1,270
Views: 104,564
Posted By sweety439
R165 at n=15K R186 at n=13K

R165 at n=15K
R186 at n=13K
Forum: Miscellaneous Math 2022-06-22, 03:04
Replies: 28
Views: 657
Posted By sweety439
I have corrected my program and searched the...

I have corrected my program and searched the residues up to mod 1000:


1: 0,
5: 3,
11: 4, 8,
19: 5, 15,
29: 6, 24,
31: 13, 19,
41: 7, 35,
Forum: Miscellaneous Math 2022-06-21, 11:42
Replies: 28
Views: 657
Posted By sweety439
e and pi are transcendental numbers .... they...

e and pi are transcendental numbers .... they cannot be calculated mod n, unless you use 355/113 instead of pi ....

the square root of 2 is imaginary number if and only if 2 is not quadratic...
Showing results 1 to 25 of 1000

 
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