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Forum: Hardware 2021-07-21, 20:47
Replies: 217
Views: 29,534
Posted By R. Gerbicz
That is suboptimal. Start the tests with some...

That is suboptimal. Start the tests with some delay, so there will be at most one in the p-1 phase.
Starting exactly 4 is problematic: say 3 of them is in the prp test (with already done p-1 phase),...
Forum: Marin's Mersenne-aries 2021-07-03, 14:28
Replies: 23
Views: 729
Posted By R. Gerbicz
Yes, that could be true. But even gpuowl...

Yes, that could be true.

But even gpuowl could do the job faster: since you get the residue for p-1 only at the end for a fused p-1/prp run you can't do a middle p-1 run.Workaround: start two p-1...
Forum: Miscellaneous Math 2021-07-02, 13:14
Replies: 12
Views: 566
Posted By R. Gerbicz
Take: N-N^(1/8)<x<=N

Take: N-N^(1/8)<x<=N
Forum: Miscellaneous Math 2021-07-02, 13:02
Replies: 12
Views: 566
Posted By R. Gerbicz
Sometimes I like the easy problems (but we're...

Sometimes I like the easy problems (but we're different) :
any 0<=x<N^(1/8) do the job.
Forum: mersenne.ca 2021-07-01, 10:19
Replies: 24
Views: 1,459
Posted By R. Gerbicz
It is on the edge, but I think that all Mp is...

It is on the edge, but I think that all Mp is squarefree. My heuristic:

For fixed p prime, we need [q=2*k*p+1 prime] q^2 | Mp.
First we have 1/log(q) probability that q is prime.
We know that...
Forum: Factoring 2021-06-30, 19:42
Replies: 3
Views: 360
Posted By R. Gerbicz
No, you need also that x1 and x2 are integers(!),...

No, you need also that x1 and x2 are integers(!), and with this it is an integer optimization problem [without easy 'shortcuts"], you can try it out using say GLPK (it is free). And it is quite well...
Forum: Software 2021-06-28, 19:49
Replies: 344
Views: 34,994
Posted By R. Gerbicz
For example on M33391 we know a pretty large d...

For example on M33391 we know a pretty large d (=p1*p2*p3*p4) divisor which enables a good error checking at least on the first stage of P+-1 : do the computation also in Z[d] and then regularly do...
Forum: Prime Gap Searches 2021-06-21, 18:08
Replies: 31
Views: 2,042
Posted By R. Gerbicz
That is great! So we were really close to this (p...

That is great! So we were really close to this (p ~ 2^64+23e15) by our exhaustive search up to 2^64 with my code (+some code improvements from users here).
Forum: Number Theory Discussion Group 2021-06-10, 01:05
Replies: 10
Views: 1,112
Posted By R. Gerbicz
a+b*I=1 looks like good for every f.

a+b*I=1 looks like good for every f.
Forum: Puzzles 2021-06-06, 00:36
Replies: 20
Views: 2,397
Posted By R. Gerbicz
An offline version of the puzzle, where you need...

An offline version of the puzzle, where you need to give all of your guesses in advance,
so you can profit nothing from the previous answers.
For n=10 here it is a solution that is using "only" 23...
Forum: Conjectures 'R Us 2021-06-04, 01:02
Replies: 952
Views: 111,846
Posted By R. Gerbicz
We are expecting that basically all of these (say...

We are expecting that basically all of these (say >1000 digits) Prps are really primes, so not composite.
Forum: Conjectures 'R Us 2021-06-04, 00:50
Replies: 952
Views: 111,846
Posted By R. Gerbicz
Not very surprising.

Not very surprising.
Forum: Puzzles 2021-06-02, 22:49
Replies: 20
Views: 2,397
Posted By R. Gerbicz
You need at least (1-eps)*n guesses on average...

You need at least (1-eps)*n guesses on average (for fixed eps>0 and for that large n).
Proof:
On the k-th level (after k guesses) there are at most (n+1)^k nodes, because each answer could be only...
Forum: YAFU 2021-06-02, 21:12
Replies: 9
Views: 622
Posted By R. Gerbicz
A small bug, on line=76 we need: ...

A small bug, on line=76 we need:

while(mpz_sgn(S)!=0){

since in the next line we'll divide by S
[in most cases we won't reach S=0 so the full continued fraction expansion because we exit much...
Forum: YAFU 2021-06-02, 20:59
Replies: 9
Views: 622
Posted By R. Gerbicz
Yes, you can use/modify etc. the code.

Yes, you can use/modify etc. the code.
Forum: YAFU 2021-06-02, 02:07
Replies: 9
Views: 622
Posted By R. Gerbicz
OK, here it is a solution, thought that it is a...

OK, here it is a solution, thought that it is a much easier code.
In a few seconds:

gerbicz@gerbicz-MS-7972:~/gmp-6.1.2$ ./f...
Forum: YAFU 2021-06-01, 21:41
Replies: 9
Views: 622
Posted By R. Gerbicz
Right, that divisor doesn't speed up the...

Right, that divisor doesn't speed up the factorisation, but here the problem is how to find that polynom if the user gives N=n/d and not the better form n.
Let me work out, but it is possible to...
Forum: YAFU 2021-06-01, 20:27
Replies: 9
Views: 622
Posted By R. Gerbicz
What about the N=n/d numbers? For example: ...

What about the N=n/d numbers? For example:

b=4241;
x=b^15;
N=(902367*x^5-2361274*x^4+32179627*x^3-45454704*x^2+545121457701*x+16647954129297)/36417887568782;
here:...
Forum: Viliam Furik 2021-05-30, 23:00
Replies: 16
Views: 615
Posted By R. Gerbicz
That would mean 1M bucks for you: ...

That would mean 1M bucks for you: https://en.wikipedia.org/wiki/Millennium_Prize_Problems. Maybe that is before tax, but I'm not really a tax expert here.
And instead of you I'd stick to these...
Forum: Software 2021-05-30, 12:45
Replies: 27
Views: 7,080
Posted By R. Gerbicz
That expensive ECC memory doesn't detect...

That expensive ECC memory doesn't detect (computational) FFT errors when you're using floating point FFT. My check detects those errors also, so you don't need to use suboptimal larger FFT size or...
Forum: Miscellaneous Math 2021-05-22, 20:26
Replies: 33
Views: 1,596
Posted By R. Gerbicz
It is: f(p)=p*log(p)*log(log(p))

It is:

f(p)=p*log(p)*log(log(p))
Forum: Miscellaneous Math 2021-05-21, 21:09
Replies: 33
Views: 1,596
Posted By R. Gerbicz
No, there should be really no connection. And...

No, there should be really no connection.
And likely there are infinitely many p, for that Mp is a Mersenne prime and p+2 is also a prime [the same is true for p-2], the heuristic calc using the...
Forum: Math 2021-05-15, 20:55
Replies: 2
Views: 549
Posted By R. Gerbicz
Multiple (prp) test at once?

When you are loading from a precomputed cos/sin table at fft or compute these in-fly then you could reuse these values. Basically hide/halve this computation cost [or just the cost of load] if you'd...
Forum: Lounge 2021-05-14, 23:50
Replies: 22
Views: 1,309
Posted By R. Gerbicz
That is true. For any N if you consider the b...

That is true.
For any N if you consider the b bases for that N is a Fermat pseudoprime then these bases form a group in Z_N.
For Mersenne numbers this means that 2^n is such a base, because mp is a...
Forum: Lounge 2021-05-04, 08:36
Replies: 40
Views: 3,529
Posted By R. Gerbicz
Thought that it is puzzle similar to: ...

Thought that it is puzzle similar to:
https://www.mersenneforum.org/showthread.php?t=4756
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