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Search: Posts Made By: R. Gerbicz
Forum: Science & Technology 2021-04-19, 10:29
Replies: 190
Views: 9,444
Posted By R. Gerbicz
Today got the first dose of AstraZeneca. Need...

Today got the first dose of AstraZeneca.
Need 12 weeks for the 2nd dose.
Forum: Math 2021-04-15, 13:59
Replies: 10
Views: 4,886
Posted By R. Gerbicz
Yes, c is irrational, but not algebraic, so you...

Yes, c is irrational, but not algebraic, so you can't apply https://en.wikipedia.org/wiki/Roth%27s_theorem . Quite a known constant, so there could be proven theorem on good/best approx for c.
Forum: Math 2021-04-13, 15:59
Replies: 10
Views: 4,886
Posted By R. Gerbicz
You need a greater precision, roughly 16 digits...

You need a greater precision, roughly 16 digits to get the correct answer for all p<10^8. Real example using Pari-Gp:

? n=181605302766736484827;
? \p
realprecision = 38 significant digits
? ...
Forum: Math 2021-04-13, 12:58
Replies: 4
Views: 173
Posted By R. Gerbicz
I've written a quite different formula. At least...

I've written a quite different formula. At least one PRP/LL test has performed on each prime for p<10^8.
Lets check out what your original formula says about the number of Mersenne primes for p in...
Forum: Math 2021-04-12, 23:09
Replies: 4
Views: 173
Posted By R. Gerbicz
Your error is in the assumptation that mp is...

Your error is in the assumptation that mp is prime by 1/log(mp) probability. The true is that it is prime by a "much" larger probability: c*log(log(mp))/log(mp) probability [what is...
Forum: Prime Gap Searches 2021-04-05, 13:51
Replies: 19
Views: 613
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: 19
Views: 613
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: 28,462
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: 401
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: 748
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: 748
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: 748
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: 838
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: 838
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: 635
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: 2,456
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: 526
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: 559
Views: 84,616
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: 304
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: 1,711
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: 1,711
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: 1,711
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: 1,711
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: 1,711
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: 7,014
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...
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