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Forum: Factoring 2022-01-19, 21:21
Replies: 3
Views: 182
Posted By R. Gerbicz
What about using a radix sort on gpu (to my...

What about using a radix sort on gpu (to my surprising it has a quite large literature), notice that here:
1. You don't need a full sort, it is enough to reach that a bucket will contain all numbers...
Forum: Math 2022-01-09, 15:27
Replies: 12
Views: 641
Posted By R. Gerbicz
In P-1 method you need that q-1 is smooth, not q...

In P-1 method you need that q-1 is smooth, not q is smooth.
Forum: And now for something completely different 2022-01-04, 15:08
Replies: 145
Views: 31,734
Posted By R. Gerbicz
That takes (at least) #n*log(p) time to check a...

That takes (at least) #n*log(p) time to check a single p prime for all #n survivors.
But we already have a faster way, that takes only polynomial time per prime: https://cr.yp.to/papers/sf.pdf
if...
Forum: Information & Answers 2022-01-01, 13:30
Replies: 32
Views: 1,428
Posted By R. Gerbicz
You forget one thing: we conjecture that the...

You forget one thing: we conjecture that the ratio of exponent's in consecutive Mersenne primes can be arbitrarily large (the record is at 127 and 521 with 521/127=4.102), ok this is a very small...
Forum: mersenne.ca 2021-12-29, 20:42
Replies: 13
Views: 422
Posted By R. Gerbicz
In c++: double getlog2(string s){ int...

In c++:

double getlog2(string s){

int L=s.length();

if(L<=16)
return log(stoll(s))/log(2);

return (log(stoll(s.substr(0,16)))+(double)(L-16)*log(10))/log(2);
Forum: mersenne.ca 2021-12-29, 10:08
Replies: 13
Views: 422
Posted By R. Gerbicz
An obvious easy/fast way to get a very good...

An obvious easy/fast way to get a very good approx for the fractional bits:
for x=a*2^e, where 0<a<2^64 the top 64 bits (for x>2^63) it is just e+log2(a), what you could get in O(1) time in gmp...
Forum: And now for something completely different 2021-12-16, 20:16
Replies: 64
Views: 11,337
Posted By R. Gerbicz
Improving all solutions: (res,m) for cpap-9...

Improving all solutions:
(res,m) for cpap-9 using only 84 primes completely eliminating the holes for composites:

Record found: th_id=6; rec=9 iteration=60708 it=10708 ii=0 time=68...
Forum: And now for something completely different 2021-12-10, 21:37
Replies: 64
Views: 11,337
Posted By R. Gerbicz
In less than 1 hour: Record found: th_id=5;...

In less than 1 hour:

Record found: th_id=5; rec=9 iteration=291167407 it=47407 time=2837...
Forum: And now for something completely different 2021-12-10, 11:00
Replies: 64
Views: 11,337
Posted By R. Gerbicz
OK, so your best is 66 holes (and what was used...

OK, so your best is 66 holes (and what was used to find your cpap-10) when the m (the step) is divisible by (exactly) primepi(257)+1=56 primes, it isn't that super useful because killing 1-2 numbers...
Forum: And now for something completely different 2021-12-09, 22:25
Replies: 64
Views: 11,337
Posted By R. Gerbicz
Should not be that 69 holes ?? ?...

Should not be that 69 holes ??

? t=1;forprime(p=2,257,t*=p);x=1153762228327967262749742078637565852209646810567096822339169424875092523431859764709708315833909447378791;
?...
Forum: Software 2021-12-09, 14:21
Replies: 351
Views: 17,272
Posted By R. Gerbicz
No, I was too compact, and a little imprecise: ...

No, I was too compact, and a little imprecise:
let new step=11*1050=11550, then
eulerphi(step)=10*240=2400,

partition the reduced residue system modulo 11550 into 10 equal size sets, where...
Forum: Software 2021-12-08, 22:50
Replies: 351
Views: 17,272
Posted By R. Gerbicz
If the init cost is small compared to the total...

If the init cost is small compared to the total cost then why wouldn't use more prime:
In this case if you'd include 11 also, then you need to evaluate in 1/11 less points with 10 times more inits...
Forum: Software 2021-12-03, 22:00
Replies: 351
Views: 17,272
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: 25
Views: 5,266
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: 2,309
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: 25
Views: 5,266
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: 1,745
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: 1,745
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: 2,309
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: 1,240
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: 1,240
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: 12
Views: 641
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: 12
Views: 641
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: 443
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: 443
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...
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