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Forum: Operazione Doppi Mersennes 2020-07-05, 17:56
Replies: 10
Views: 554
Posted By R. Gerbicz
Yes, that is a divisor: ?...

Yes, that is a divisor:

? d=886407410000361345663448535540258622490179142922169401;
? Mod(2,d)^(2^127-1)+1
%2 = Mod(0, 886407410000361345663448535540258622490179142922169401)
? ##
*** last...
Forum: Math 2020-06-23, 09:12
Replies: 195
Views: 8,014
Posted By R. Gerbicz
With those recursive calls it will use power...

With those recursive calls it will use power residues in stack memory.
Is it intended? You could do this also in disk (using the same size).
Forum: Math 2020-06-23, 01:43
Replies: 195
Views: 8,014
Posted By R. Gerbicz
You could use sliding window technique in void...

You could use sliding window technique in void exponentiate (gwhandle *gwdata, gwnum x, uint64_t power) .
Forum: Puzzles 2020-06-22, 09:50
Replies: 7
Views: 219
Posted By R. Gerbicz
I've also that in my mind. Generated 1e8 random...

I've also that in my mind. Generated 1e8 random boards, and counted 8499941 configurations that has no 5 or more same piece in a line. So roughly we are expecting 0.085*binomial(80,40) for the whole...
Forum: Puzzles 2020-06-22, 06:33
Replies: 7
Views: 219
Posted By R. Gerbicz
So there is no at least 5 in a line?

So there is no at least 5 in a line?
Forum: Puzzles 2020-06-21, 22:56
Replies: 7
Views: 226
Posted By R. Gerbicz
A faster approach: if the discriminant is not a...

A faster approach: if the discriminant is not a square then you can eliminate that triplet. With that you don't even need to calculate the coefficients, just check for ~50 smallest primes if the...
Forum: Math 2020-06-20, 10:11
Replies: 195
Views: 8,014
Posted By R. Gerbicz
You can easily avoid this just set hash=2*hash+1,...

You can easily avoid this just set hash=2*hash+1, even if you'd this for every computed hash then no hash value will be zero among h_i.
Forum: News 2020-06-20, 05:53
Replies: 99
Views: 3,959
Posted By R. Gerbicz
With power=5 would you need more than 3%...

With power=5 would you need more than 3% verification time of the original prp test.
Forum: News 2020-06-19, 19:58
Replies: 99
Views: 3,959
Posted By R. Gerbicz
If you want a flexible check, where the...

If you want a flexible check, where the L=interval used for check is not fixed then you need to save the base, where you restarted the check with a new L. You can restart at every error checked...
Forum: Miscellaneous Math 2020-06-18, 18:47
Replies: 20
Views: 418
Posted By R. Gerbicz
Let s(n)=sigma(n)-n the aliquot function, the OP...

Let s(n)=sigma(n)-n the aliquot function, the OP mentioned that s(3*p^2) is a square if p!=3 prime.
And the connection: if n is an even perfect(!) number then s(2*n) is a perfect(!) square.
Forum: Math 2020-06-17, 20:19
Replies: 195
Views: 8,014
Posted By R. Gerbicz
Nice colorful picture, though there is very few...

Nice colorful picture, though there is very few formula (zero) in that pic. And I've already shown that it does not prove that all residues are correct.
Forum: Math 2020-06-17, 19:19
Replies: 195
Views: 8,014
Posted By R. Gerbicz
It doesn't imply for any h value: to pass the...

It doesn't imply for any h value: to pass the test (for E=1) you need
(A^h*M)^(2^(top/2)) == M^h*B mod N

but if you fix M then you can choose B in a unique way, so it has N solutions, but that is...
Forum: News 2020-06-17, 19:06
Replies: 99
Views: 3,959
Posted By R. Gerbicz
You're right, one big advantage of setting r_i=1...

You're right, one big advantage of setting r_i=1 is that it has a nice "ladder" scheme, enabling a fast product calculation and (multiple) error checking.
With the proof basically you are doing one...
Forum: kriesel 2020-06-16, 15:21
Replies: 8
Views: 313
Posted By R. Gerbicz
Do not(!!!) vote for "Mersenne CoFactor PRP with...

Do not(!!!) vote for "Mersenne CoFactor PRP with Gerbicz check"
basically you can do this in gpuowl, just start a prp test, if the final residue is 3^(mp+1)==res mod mp, then you need
3^(d+1)==res...
Forum: Math 2020-06-14, 07:38
Replies: 195
Views: 8,014
Posted By R. Gerbicz
That doesn't needs uploading 2^power full...

That doesn't needs uploading 2^power full residues per test?
Forum: Math 2020-06-14, 05:58
Replies: 195
Views: 8,014
Posted By R. Gerbicz
You forget the topK/2^e squarings. And there is...

You forget the topK/2^e squarings. And there is no other cost in the proof.



Maybe the original paper talked about 64 bit values, I'd say 16 bits would be still OK.
Forum: Math 2020-06-13, 22:27
Replies: 195
Views: 8,014
Posted By R. Gerbicz
You can do those costly residue^product(h)...

You can do those costly residue^product(h) computations in the proof much faster than the described trivial way. And basically the same trick worked what I've already written in a post. After writing...
Forum: Factoring 2020-06-09, 11:40
Replies: 13
Views: 591
Posted By R. Gerbicz
My Pari gives: ? (-1064)%109 %12 = 26 ? ...

My Pari gives:

? (-1064)%109
%12 = 26
?

It is a quite antique installation, but I believe in its result.
Forum: Math 2020-06-08, 18:17
Replies: 195
Views: 8,014
Posted By R. Gerbicz
I thought that too (so for prime N there is...

I thought that too (so for prime N there is nothing interesting), but it is false for the prime N=997, 2nd follow-up let's consider the 921,151 pair (again the true residue pair was 249,804).

?...
Forum: Math 2020-06-08, 17:37
Replies: 195
Views: 8,014
Posted By R. Gerbicz
The true pair was (249,804), in the follow-up...

The true pair was (249,804), in the follow-up consider another pair (748,193):

? check_proof(748,193,997,500)
Test#1: h=780 failed the test
Test#2: h=613 passed the test
Test#3: h=978 failed...
Forum: Math 2020-06-04, 08:40
Replies: 195
Views: 8,014
Posted By R. Gerbicz
There are flaws in that post, but probably all...

There are flaws in that post, but probably all previous posts were good, used the same notations from Preda: https://mersenneforum.org/showpost.php?p=546553&postcount=15

the verification for a...
Forum: Math 2020-06-04, 07:23
Replies: 195
Views: 8,014
Posted By R. Gerbicz
There is nothing special in 997, for...

There is nothing special in 997, for composite/prime the proof check should run in the same way.


Asked one. But let's take not the first because you could complain why. Picked the (5,718)

...
Forum: Math 2020-06-03, 19:52
Replies: 195
Views: 8,014
Posted By R. Gerbicz
Ok, a very small test, but this is better than...

Ok, a very small test, but this is better than the usual tests with multi million digits.
So fake me:
Fix the base=A=3, we are claiming that
M=3^(2^(top/2)) mod N
B=3^(2^top) mod N

for N=997...
Forum: Math 2020-06-03, 00:16
Replies: 195
Views: 8,014
Posted By R. Gerbicz
They consider more r-th roots, not only (in our...

They consider more r-th roots, not only (in our case) the (2^d-1)-th root. But regarding only this form allows us to compute the (2^d-1)-th root with just d+p/d mulmods if we have stored p/L residues...
Forum: Math 2020-06-02, 18:12
Replies: 195
Views: 8,014
Posted By R. Gerbicz
Challenge-response type of proof using only 2*p...

Challenge-response type of proof using only 2*p bits of memory sent to the server (that would send it to the verifier), and with ~1/1024 chance to fake it by a clever cheater (assuming a single...
Showing results 1 to 25 of 1000

 
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