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Search: Posts Made By: R. Gerbicz
Forum: Prime Gap Searches 2021-04-05, 13:51
Replies: 18
Views: 496
Posted By R. Gerbicz
For that record used only your 1st method with...

For that record used only your 1st method with the following modification:
collect in array/vector those res values that occur maximal times as x%p and choose randomly(!) one res value from these....
Forum: Prime Gap Searches 2021-04-02, 23:22
Replies: 18
Views: 496
Posted By R. Gerbicz
Improved solution with 6727 numbers survived the...

Improved solution with 6727 numbers survived the sieve:
...
Forum: YAFU 2021-03-24, 22:48
Replies: 62
Views: 27,410
Posted By R. Gerbicz
Found these two posts from different threads: ...

Found these two posts from different threads:
https://www.mersenneforum.org/showpost.php?p=54147&postcount=33
https://www.mersenneforum.org/showpost.php?p=530352&postcount=23
Forum: PrimeNet 2021-03-22, 23:06
Replies: 8
Views: 345
Posted By R. Gerbicz
These were discussed multiple times. A new thing...

These were discussed multiple times. A new thing to demonstrate that the shiftcount trick is actually not enough!
We claim that mult(x,y,p) returns (x*y)%(2^p-1), and implement [correctly!] the...
Forum: Hardware 2021-03-21, 17:00
Replies: 16
Views: 724
Posted By R. Gerbicz
Checkout that p95 can change the blocksize, I...

Checkout that p95 can change the blocksize, I don't see any advantage to fix it.


Yes, that is true.

I have overlooked that as I can remember gpuowl is a little tricky in this area, because it...
Forum: Hardware 2021-03-21, 12:13
Replies: 16
Views: 724
Posted By R. Gerbicz
Looks like my above formula is good, my...

Looks like my above formula is good, my reasoning:
we have q=(1-e)^B probability that in a single block all B iterations is good. You have 2*sqrt(B) iterations to do the in the check per block,
and...
Forum: Hardware 2021-03-19, 21:07
Replies: 16
Views: 724
Posted By R. Gerbicz
Suboptimal run, with those many errors you could...

Suboptimal run, with those many errors you could get a very good approx for the error rate and using that you/we could optimize the block size to lower the expected number of iterations.

Check me:...
Forum: Other Mathematical Topics 2021-03-11, 17:14
Replies: 27
Views: 796
Posted By R. Gerbicz
It is a perfect counterexample to your claim in...

It is a perfect counterexample to your claim in the first post. Likely a=11 seems to be equally good just as a=3, maybe there is no other counterexample for a=11. Let me check [only the first few odd...
Forum: Other Mathematical Topics 2021-03-11, 16:16
Replies: 27
Views: 796
Posted By R. Gerbicz
So you want to say that if a^((mp-1)/2)==-1 mod...

So you want to say that if a^((mp-1)/2)==-1 mod mp for given a>2 then mp is prime.
It would follow that Mp is always prime(!), just use a=-1+mp. To see a non-trivial counterexample: let a=11 and...
Forum: Miscellaneous Math 2021-03-04, 18:03
Replies: 15
Views: 569
Posted By R. Gerbicz
Destroyed? rate=0.1;year=21;(1+rate)^year ...

Destroyed?

rate=0.1;year=21;(1+rate)^year
rate=0.03;year=3;(1-(1+rate)^(-year))/rate

answer:
%1 = 7.4002499442581601012110000000000000000
%2 = 2.8286113548946809221333416306177114687
Forum: Factoring 2021-03-03, 15:21
Replies: 13
Views: 2,259
Posted By R. Gerbicz
An early slide from him:...

An early slide from him: https://eurocrypt2009rump.cr.yp.to/e074d37e10ad1ad227200ea7ba36cf73.pdf

Forums about these claims:...
Forum: Miscellaneous Math 2021-03-02, 20:32
Replies: 7
Views: 494
Posted By R. Gerbicz
Very standard heuristic idea gives that we are...

Very standard heuristic idea gives that we are expecting very few [maybe zero] composites for G=nextprime(n!)-n! [if we exclude the G<2 cases].

As you noted to find composite G we need G>n^2 so...
Forum: Data 2021-02-24, 20:17
Replies: 558
Views: 82,411
Posted By R. Gerbicz
We had already a Prp-cf test on this: ...

We had already a Prp-cf test on this:
https://www.mersenne.org/report_exponent/?exp_lo=82939&exp_hi=&full=1

Notice that for N=(k*2^n+c)/d we're using a Fermat test using
base^d as base, then...
Forum: Miscellaneous Math 2021-02-20, 09:53
Replies: 4
Views: 289
Posted By R. Gerbicz
Repeated digit sum has a name:...

Repeated digit sum has a name: https://en.wikipedia.org/wiki/Digital_root .
Forum: Miscellaneous Math 2021-02-19, 20:18
Replies: 32
Views: 1,674
Posted By R. Gerbicz
Nice. You can negate that: x=F(n-1)/(F(n-2)-1)...

Nice. You can negate that: x=F(n-1)/(F(n-2)-1) mod F(n)

And in general: if n=u^4+1 then for x=(u^2+1)/u:
x^2==2 mod n.
Forum: Miscellaneous Math 2021-02-19, 15:18
Replies: 32
Views: 1,674
Posted By R. Gerbicz
Yes, that was my method.

Yes, that was my method.
Forum: Miscellaneous Math 2021-02-19, 10:36
Replies: 32
Views: 1,674
Posted By R. Gerbicz
And with linear algebra would you need...

And with linear algebra would you need primepi(100)+eps=25+eps relations ?
OK, take my challenge factor my GRSA100 [G means Gerbicz], n=p*q number with 100 digits. You can use "your" method, and...
Forum: Miscellaneous Math 2021-02-19, 08:22
Replies: 32
Views: 1,674
Posted By R. Gerbicz
Yes, used those known factors, but how? I mean if...

Yes, used those known factors, but how? I mean if M|N then we know only small squared residues mod M in the range of sqrt(M), but we need these residues mod N and not mod M. Ofcourse you can regard...
Forum: Miscellaneous Math 2021-02-19, 01:00
Replies: 32
Views: 1,674
Posted By R. Gerbicz
Actually it is easy, using the OP's other...

Actually it is easy, using the OP's other favourite number: F12 Fermat number [which was unfactored yesterday]:


N=2^4096+1;...
Forum: Information & Answers 2021-02-15, 17:10
Replies: 26
Views: 6,966
Posted By R. Gerbicz
Oh, yes that is even better what I've written,...

Oh, yes that is even better what I've written, and maybe: forcing that the server wouldn't give out the same prime exponent twice per day. In this way even if you have a fully factorized mp you would...
Forum: Information & Answers 2021-02-14, 23:39
Replies: 26
Views: 6,966
Posted By R. Gerbicz
Interesting topic. Still don't see a way, my...

Interesting topic. Still don't see a way, my failed approach in the prp(!) setup:

The key idea is to change the base after a successful mining to a random base with say 64 bits.
And then the new...
Forum: Homework Help 2021-02-13, 21:46
Replies: 3
Views: 484
Posted By R. Gerbicz
If x is composite then we know: ...

If x is composite then we know:
c*x/log(log(x))<phi(x)<=x-sqrt(x), where c>0 is a constant [c=0.25 is good for all x>6].

ok, not very elegant to use these, though this is still elementary.
With...
Forum: Chess 2021-01-31, 19:40
Replies: 12
Views: 1,376
Posted By R. Gerbicz
Yes, forget that above we need to store also the...

Yes, forget that above we need to store also the number of bits of x. Here 15 or 16 bits should be enough maybe for all games.
Forum: Chess 2021-01-31, 15:02
Replies: 12
Views: 1,376
Posted By R. Gerbicz
Even easier way if you want to encode only a...

Even easier way if you want to encode only a single/few game:
use a generalized number system, say in the i-th move you have only B[i] valid moves you have chosen the r[i]-th move from these. And...
Forum: Chess 2021-01-31, 13:02
Replies: 12
Views: 1,376
Posted By R. Gerbicz
You can reach almost the optimal log(13)/log(2)...

You can reach almost the optimal log(13)/log(2) bits difficulty when you have 13 possibilities
for a move. The idea is that for each p number of possibility maintain a seperate array to
extract the...
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