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Forum: Analysis & Analytic Number Theory 2020-09-21, 15:41
Replies: 7
Views: 235
Posted By R. Gerbicz
It is a triviality, once you know the sum of a...

It is a triviality, once you know the sum of a geometric serie, could be known for 2400 years. To make things easier split the proof for odd/even n.
Forum: Abstract Algebra & Algebraic Number Theory 2020-09-20, 20:33
Replies: 6
Views: 230
Posted By R. Gerbicz
See also for lots of big arctan formulas:...

See also for lots of big arctan formulas: http://www.machination.eclipse.co.uk/FSChecking.html
(last update was at 2013)
Forum: Abstract Algebra & Algebraic Number Theory 2020-09-20, 20:17
Replies: 6
Views: 230
Posted By R. Gerbicz
See: http://oeis.org/A185389 (somewhere there...

See: http://oeis.org/A185389 (somewhere there could be a longer computed list also).
This problem is solvable by https://en.wikipedia.org/wiki/St%C3%B8rmer%27s_theorem using a Pell type equation,...
Forum: Analysis & Analytic Number Theory 2020-09-20, 16:58
Replies: 7
Views: 235
Posted By R. Gerbicz
It says that there are floor(2^n+10)/6 quadratic...

It says that there are floor(2^n+10)/6 quadratic residues mod 2^n.


You need 4 squares for x iff x=4^e*(8*k+7) it is pretty old fact.
If you want the count for this for x<2^n then you can set...
Forum: Miscellaneous Math 2020-09-15, 14:50
Replies: 12
Views: 319
Posted By R. Gerbicz
I've thought that I understand you, but not....

I've thought that I understand you, but not. Learn more Maths, and more English.
Forum: Miscellaneous Math 2020-09-15, 13:58
Replies: 12
Views: 319
Posted By R. Gerbicz
Yes, that is true, since if N denotes your number...

Yes, that is true, since if N denotes your number then N+2 is divisible by 3 and N-2 is divisible by 107.
Forum: GpuOwl 2020-09-08, 23:24
Replies: 58
Views: 2,041
Posted By R. Gerbicz
Hm, but if you use my prp cf method then you can...

Hm, but if you use my prp cf method then you can save that annoying large division. So compute just
(3^mp mod mp) mod 2^2048 (or 3^(1+mp)... ) just as if we'd know only d=1, and then apply my prp...
Forum: GpuOwl 2020-09-08, 22:59
Replies: 58
Views: 2,041
Posted By R. Gerbicz
Exactly, what I don't understand is that why...

Exactly, what I don't understand is that why anyone tries to run something that is clearly not supported, and you can check this easily at https://github.com/preda/gpuowl . It means nothing that it...
Forum: Puzzles 2020-08-30, 15:17
Replies: 20
Views: 997
Posted By R. Gerbicz
Congrats, and you could easily generalize it:...

Congrats, and you could easily generalize it: this time using only 6 and 9 in the last 50 places

? Mod(2,10^50)^5342684466535587793434484498741672
%26 =...
Forum: Puzzles 2020-08-30, 12:49
Replies: 20
Views: 997
Posted By R. Gerbicz
Like these challenges, and how would you kill...

Like these challenges, and how would you kill this example:
power of two ending last 50 digits using only 1-2:

? Mod(2,10^50)^18530118576724016889332506805003089
%36 =...
Forum: Factoring 2020-08-26, 19:50
Replies: 6
Views: 612
Posted By R. Gerbicz
And then msieve is faster than light? Save out...

And then msieve is faster than light?
Save out logs.length to a parameter. Don't know Java, but similar code in c++ is also slower when I'm using .size() in a loop.
Forum: Math 2020-08-24, 23:56
Replies: 37
Views: 1,704
Posted By R. Gerbicz
Another great success was the PRP CF proof idea...

Another great success was the PRP CF proof idea from me. It could be a joint paper, but I've not a lot of time for it, maybe I could start and finish it this year. Mathematics of Computation would be...
Forum: Miscellaneous Math 2020-08-19, 02:18
Replies: 88
Views: 7,735
Posted By R. Gerbicz
8 Mb memory is more than enough, what Pari Gp...

8 Mb memory is more than enough, what Pari Gp starts on my system:

parisize = 8000000, primelimit = 500000
? p=60651732991;e=20;V=Vec(lift(Mod(x,x^2-2*x-2)^2^e));
print([p,(V[1]+V[2])==0])
?...
Forum: Puzzles 2020-08-19, 01:44
Replies: 28
Views: 1,786
Posted By R. Gerbicz
I've found another algorithm to compute...

I've found another algorithm to compute g^exponent once you are given all g^(2^k) [mod N]. Turned out it is using more mulmods, but this still depends how efficiently you partition the bits=1 in the...
Forum: Lounge 2020-08-15, 09:58
Replies: 11
Views: 724
Posted By R. Gerbicz
When you have the proof scheme then probably...

When you have the proof scheme then probably nothing, but say 1% if you have no proof scheme (it is still too generous as the prp has much less than 1% failure).
One advantage of a factor is that...
Forum: Lounge 2020-08-15, 08:51
Replies: 11
Views: 724
Posted By R. Gerbicz
A lot, maybe even 800% or more (for small...

A lot, maybe even 800% or more (for small exponent). Why? Because for semi prime Mersenne number even a single factor means that you have a full factorization. OK, without the proof that the factors...
Forum: Combinatorics & Combinatorial Number Theory 2020-08-14, 22:05
Replies: 5
Views: 940
Posted By R. Gerbicz
Probably there is no advantage for that, but any...

Probably there is no advantage for that, but any odd factor of Mp-1 could give a non-trival factor of another Mersenne number (with prime index),
since r|Mp-1=2*(2^(p-1)-1).
Forum: Math 2020-08-13, 10:24
Replies: 3
Views: 594
Posted By R. Gerbicz
Yes, a numeric evaluation, integration is quite...

Yes, a numeric evaluation, integration is quite easy.
But an analytic formula for a fixed [n-1,n] (or subinterval) is still possible, I've done exactly the same way to get the above rho(x) when done...
Forum: Math 2020-08-12, 12:06
Replies: 3
Views: 594
Posted By R. Gerbicz
You can get the rho function's Taylor polynom for...

You can get the rho function's Taylor polynom for each n in the [n-1,n] interval, if you want the first n=maxn polynom, then just call ff(maxn,maxe) if you want the max degree=e in the polynoms, I've...
Forum: GpuOwl 2020-08-07, 16:10
Replies: 2,496
Views: 147,824
Posted By R. Gerbicz
Basically that prp-cf test it the same as the prp...

Basically that prp-cf test it the same as the prp test, just in the end there is a big division.
Even if the server already accepted such runs from your gpuowl (is it/was it possible?), then it is...
Forum: Puzzles 2020-08-06, 23:05
Replies: 28
Views: 1,786
Posted By R. Gerbicz
Checked those 480780, 100622 numbers. Turned out...

Checked those 480780, 100622 numbers. Turned out that it is using more multiplications, I counted every mults, and to get the final product from the y[] array you also need mults. I mean this is not...
Forum: Puzzles 2020-08-06, 20:58
Replies: 28
Views: 1,786
Posted By R. Gerbicz
What addition chains here is now obsolete in the...

What addition chains here is now obsolete in the method. See one of my post, the required final task for E=2 to get:
R=y[1]*y[3]^3*y[5]^5*y[7]^7 mod M.
Forum: Puzzles 2020-08-06, 20:18
Replies: 28
Views: 1,786
Posted By R. Gerbicz
Yes, I've used the popular sliding window name,...

Yes, I've used the popular sliding window name, but here there is no such precomputation here. Yeah it is hard to believe there is such an algorithm, because in that sliding window you are actually...
Forum: Puzzles 2020-08-06, 19:42
Replies: 28
Views: 1,786
Posted By R. Gerbicz
Searched today exactly that crypto paper, thanks....

Searched today exactly that crypto paper, thanks.
I'll check it.
Forum: Puzzles 2020-08-06, 17:54
Replies: 28
Views: 1,786
Posted By R. Gerbicz
Really don't understand, could you explain it? ...

Really don't understand, could you explain it?
But I've just revisited my pari code and forget to subtract one, so my updated code gives only 104341 multiplications for E=13 (and that is still the...
Showing results 1 to 25 of 1000

 
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