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Search: Posts Made By: R. Gerbicz
Forum: Software 2021-12-03, 22:00
Replies: 90
Views: 1,465
Posted By R. Gerbicz
What is the third number on this line: "D: 1050,...

What is the third number on this line: "D: 1050, 120x403 polynomial multiplication."
just guessing that the 2nd is eulerphi(1050)/2=120, but what is the 403 ?
Forum: Homework Help 2021-11-27, 16:10
Replies: 24
Views: 4,292
Posted By R. Gerbicz
Modified your idea, close to a pure combinatorial...

Modified your idea, close to a pure combinatorial proof:

The k=0 case is trivial, so assume that 0<k<p,
it is known: binomial(p-1,k-1)+binomial(p-1,k)=binomial(p,k) [for here you don't need that...
Forum: Wagstaff PRP Search 2021-11-26, 21:04
Replies: 7
Views: 652
Posted By R. Gerbicz
Wagstaff numbers are pretty special cyclotomic...

Wagstaff numbers are pretty special cyclotomic numbers, these are polcyclo(2*p,2)=(2^p+1)/3.
There is no known fast tests (at speed of LL test), though there could be! Note that here for example...
Forum: Homework Help 2021-11-26, 19:49
Replies: 24
Views: 4,292
Posted By R. Gerbicz
I see where you could use Wilson theorem in the...

I see where you could use Wilson theorem in the problem, though those solutions would be a little ugly. But really don't see what is in the next chapter and what you could/should use.
Freely use...
Forum: Programming 2021-11-25, 21:08
Replies: 4
Views: 414
Posted By R. Gerbicz
Up to constant factor it should be the same...

Up to constant factor it should be the same speed.
Then analyse how much memory your code needs. Also if you'd contruct all integers in that way then your code runs in quadratic time and needs much...
Forum: Programming 2021-11-25, 19:03
Replies: 4
Views: 414
Posted By R. Gerbicz
You need only mpz_setbit(), this is optimal in...

You need only mpz_setbit(), this is optimal in speed/complexity, (you set the ones in the expansion).

For example this runs in 0 second: (maybe you should build up from the other direction,...
Forum: Wagstaff PRP Search 2021-11-25, 18:41
Replies: 7
Views: 652
Posted By R. Gerbicz
It will become a viable test when you prove that...

It will become a viable test when you prove that it generates all Wagstaff primes, and gives no composites. Until that it is "only" a claim.
Thanks:)
Forum: Number Theory Discussion Group 2021-11-23, 15:03
Replies: 15
Views: 750
Posted By R. Gerbicz
Here it is that free article:...

Here it is that free article: https://www.ams.org/journals/mcom/1989-52-185/S0025-5718-1989-0946602-9/S0025-5718-1989-0946602-9.pdf
You want to use theorem 6, then check it again, what they write,...
Forum: Number Theory Discussion Group 2021-11-22, 20:42
Replies: 15
Views: 750
Posted By R. Gerbicz
We use different letters, but never mind. For...

We use different letters, but never mind.
For q=3 (p=7) your test fails, otherwise it is good up to at least q=1000.
I don't know how it could be good with correct proof after q=3 (not checked the...
Forum: Math 2021-11-22, 15:15
Replies: 9
Views: 294
Posted By R. Gerbicz
Yes, it is pure luck, basically you have...

Yes, it is pure luck, basically you have something 1/(B1*log(B1)) probability to see this lucky find (in this calc we don't assume that there is exactly one prime factor>B1).

Another type of...
Forum: Math 2021-11-22, 14:26
Replies: 9
Views: 294
Posted By R. Gerbicz
The OP's question is still valid, you can really...

The OP's question is still valid, you can really find a factor for that p-1 is not smooth, beyond the B1 limit (with ofcourse excluding here the special factors for special numbers). Example:
use...
Forum: Math 2021-11-21, 16:55
Replies: 4
Views: 294
Posted By R. Gerbicz
Yes, and with that oldish certificates you would...

Yes, and with that oldish certificates you would only double check the first computation, what Gimps has done in the past. Then call the new method as fast certificate, because you need there roughly...
Forum: Math 2021-11-21, 13:32
Replies: 4
Views: 294
Posted By R. Gerbicz
OP wants something different. A primality...

OP wants something different. A primality certificate for Mersenne primes, so a (very) fast proof when 2^p-1 is prime (where p is an odd prime).

Let r=2+sqrt[3] and calculate v=r^(2^(p-2)) in...
Forum: Homework Help 2021-11-20, 16:37
Replies: 24
Views: 4,292
Posted By R. Gerbicz
That is...

That is https://en.wikipedia.org/wiki/Euler%27s_theorem for m=p^n. When you want the best exponent for all gcd(a,n)=1 it is also a known problem (n=168 in your case).

Let...
Forum: Miscellaneous Math 2021-11-16, 14:18
Replies: 7
Views: 283
Posted By R. Gerbicz
For any p the e values is not lower bounded: ...

For any p the e values is not lower bounded:
set say x=1, then x^2*(x^3+y^3)=y^3+1 goes to -inf for y->-inf.

For your 2nd question: about solving the equation for a given n=p+e:
x^2*(x^3+y^3)=n...
Forum: Number Theory Discussion Group 2021-11-15, 21:28
Replies: 30
Views: 5,710
Posted By R. Gerbicz
Yeah, you're really messed up with a trivial...

Yeah, you're really messed up with a trivial algorithm, a corrected one: (here you don't need to use ptr, so pointers, but give a clean code)

void mpz_mod_mp (mpz_ptr r, mpz_ptr a, mp_bitcnt_t p)...
Forum: Information & Answers 2021-11-15, 17:50
Replies: 18
Views: 1,286
Posted By R. Gerbicz
Nice, not remembered for this, but for "large" n...

Nice, not remembered for this, but for "large" n the k*2^n-1+1,+5 formula shouldn't be winning due to the slightly faster prp tests on special form?
You would need T(N)=O(log(N)^5/loglog(N)^2) bit...
Forum: Puzzles 2021-11-15, 15:12
Replies: 31
Views: 15,561
Posted By R. Gerbicz
Thanks for the idea, then I'll try the AMM first,...

Thanks for the idea, then I'll try the AMM first, need to write down the solution.
It is a somewhat recreational Maths problem, but worth a paper.
Forum: Homework Help 2021-11-15, 14:57
Replies: 2
Views: 319
Posted By R. Gerbicz
You want this page from Iron Age:...

You want this page from Iron Age: https://primes.utm.edu/notes/faq/NextMersenne.html
for even(!) perfect numbers you get a similar graph, since P(k)=2^(p-1)*(2^p-1)~0.5*Mp^2
and for that...
Forum: Factoring 2021-11-09, 22:00
Replies: 17
Views: 904
Posted By R. Gerbicz
Much better: sieve and search only b=k*2^762...

Much better: sieve and search only
b=k*2^762 for k>10^15 (you can limit to say k<2^64).
This will be good since now b is easily fully factored (you need to factor only k, but that is trivial).
and...
Forum: Software 2021-11-06, 15:54
Replies: 10
Views: 784
Posted By R. Gerbicz
I'm not sure what your code is doing, anyway, for...

I'm not sure what your code is doing, anyway, for a fixed B bound and e>1, solve the
x*log(x)/e=B*log(B)
equation, say binary search is fine since x*log(x) is monotone increasing (on [exp(-1),inf)...
Forum: Software 2021-11-04, 18:09
Replies: 10
Views: 784
Posted By R. Gerbicz
correction: log2(T)=187.0 sum(1/q^e)=0.00018 ...

correction:
log2(T)=187.0
sum(1/q^e)=0.00018
and effective score=995837.4 what is smaller than the base score:
log2(B)*B=1660964.05
Forum: Software 2021-11-04, 17:16
Replies: 10
Views: 784
Posted By R. Gerbicz
Today multiple times I felt the same, but...

Today multiple times I felt the same, but currently I think that this is a working idea, even in P+1/ecm ! Would give a tiny speedup. Let me check my suggestion.
In the general way: for a given...
Forum: Puzzles 2021-11-02, 10:51
Replies: 31
Views: 15,561
Posted By R. Gerbicz
There was a request to explain this more, took me...

There was a request to explain this more, took me some time to understand some tricks.

First why parity is so important here. It is trivial: for each c=-24..24 we choose T(c,0) or T(c,1), exactly...
Forum: Software 2021-10-25, 18:25
Replies: 598
Views: 87,120
Posted By R. Gerbicz
Just for curiosity that is is how many k/n pairs,...

Just for curiosity that is is how many k/n pairs, so what is the #k * (nmax-nmin) ?
Showing results 1 to 25 of 1000

 
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