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Search: Posts Made By: T.Rex
Forum: Math 2021-11-30, 22:15
Replies: 9
Views: 368
Posted By T.Rex
Hello. I've spent some time searching for...

Hello.
I've spent some time searching for Universal Seeds for the LLT-like test for Wagstaff numbers.
Here attached is a first set of findings.
Everything has been checked for all known Wagstaff...
Forum: Math 2021-11-27, 08:54
Replies: 9
Views: 368
Posted By T.Rex
Good ! Thanks ! I should have checked...

Good !
Thanks !
I should have checked Yesterday.
Forum: Math 2021-11-27, 08:52
Replies: 9
Views: 368
Posted By T.Rex
Not exactly. There are 2^x (cannot remember the...

Not exactly. There are 2^x (cannot remember the exact value, x depends on q, and I'm now typing on my phone) seeds for each Mq. But there are only 3 F IXED values which can be used for all Mq.

I...
Forum: Math 2021-11-26, 22:14
Replies: 9
Views: 368
Posted By T.Rex
Universal seeds of the LLT for Mersenne and Wagstaff numbers

You probably know that there are 3 Universal Seeds for starting the LLT for Mersenne numbers: 4, 10, and 2/3.
It appears that 2/3 modulo Mq = (2^q+1)/3 = Wq, a Wagstaff number.

Also, you may know...
Forum: Miscellaneous Math 2021-09-15, 04:23
Replies: 12
Views: 3,267
Posted By T.Rex
Hummmm Right. My 2nd comment was stupid based...

Hummmm Right.
My 2nd comment was stupid based on the first one.
First one seems to say that there is no rule enabling to find the next Mersenne prime based on the knowledge of previous known...
Forum: Miscellaneous Math 2021-09-15, 03:06
Replies: 12
Views: 3,267
Posted By T.Rex
I found this papier very interesting: ...

I found this papier very interesting:
https://faculty.math.illinois.edu/~jli135/paper/MersenneBenford.pdf
First, it seems to say that Mersenne primes are random.

Second, it means that looking at...
Forum: And now for something completely different 2021-04-21, 03:00
Replies: 71
Views: 8,652
Posted By T.Rex
Wowww So Big. Congratulations!

Wowww So Big. Congratulations!
Forum: Wagstaff PRP Search 2021-03-20, 18:18
Replies: 5
Views: 7,504
Posted By T.Rex
Hi tetramur, I've just seen your post. I need...

Hi tetramur,
I've just seen your post. I need to refresh my few Maths skills before saying anything. And probably that I'll not be able to say if it is correct or not.
Anyway, I'm happy to see that...
Forum: Wagstaff PRP Search 2020-08-18, 22:15
Replies: 7
Views: 6,296
Posted By T.Rex
Let's also note that the product of all s: ...

Let's also note that the product of all s:
for i=1 to q-2, when p==5 mod 6, equals 1
for i=1 to q-1, when p==1 mod 6, equals -1
We have a similar property when using Vbra-Reix, starting at...
Forum: Wagstaff PRP Search 2020-08-18, 20:39
Replies: 7
Views: 6,296
Posted By T.Rex
Looking at: https://oeis.org/A018844 it appears...

Looking at: https://oeis.org/A018844 it appears that Wagstaff and Mersenne numbers share half the same seeds: 4, 52, 724, ... {Each seed n is such that n-2=2*(m^2) and n+2=[3or6]*(p^2) where m and p...
Forum: Wagstaff PRP Search 2020-08-18, 18:18
Replies: 7
Views: 6,296
Posted By T.Rex
This holds also when 4 is replaced by: 52, 724, ...

This holds also when 4 is replaced by: 52, 724, 10084, 140452, 1956244, or 27246964 .

Found by means of (Pari/gp):

L = [5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 43, 61, 79, 101, 127, 167,...
Forum: Wagstaff PRP Search 2019-11-22, 15:32
Replies: 6
Views: 3,833
Posted By T.Rex
(New ?) Wagstaff/Mersenne related property

Hi,

I have no idea if this property is new. If new, I even am not sure it may be useful.
Anyway.

Let q prime >3
q=2p+1 and thus p=\frac{q-1}{2}.

Let:
N_p=2^p+1 .
Forum: Lounge 2016-02-17, 20:49
Replies: 133
Views: 9,962
Posted By T.Rex
ADDRESS VERIFIED: YES MISSING: NONE PACKAGED:...

ADDRESS VERIFIED: YES
MISSING: NONE
PACKAGED: YES
SENT: 24 MAR
RECEIVED:
Forum: Miscellaneous Math 2015-10-16, 19:02
Replies: 27
Views: 3,132
Posted By T.Rex
I still think that an algorithm that produces...

I still think that an algorithm that produces only 3 kinds of numbers:
1) primes
2) composite numbers like the ones here below (only 1 small divisor equal to 2b-1)
3) cases in bold (like...
Forum: Miscellaneous Math 2015-09-11, 19:13
Replies: 27
Views: 3,132
Posted By T.Rex
I'm Hobbes ! A real Tiger !! Be afraid ! And read...

I'm Hobbes ! A real Tiger !! Be afraid ! And read again all Watterson's books in order to remember how dangerous I can be !!

;)
Forum: Miscellaneous Math 2015-09-09, 20:41
Replies: 27
Views: 3,132
Posted By T.Rex
Here is a modified code that shows the...

Here is a modified code that shows the pseudoprimes such that N=0 mod(2*c-1) :

CEk2c(k,c,g)=
{
a=6;
h=a/2;
if(c>0,s=1,s=-1;c*=-1);
for(n=c<<1+1,g,
N=k<<n+s*c;
e=c%4;
Forum: Miscellaneous Math 2015-09-09, 13:23
Replies: 27
Views: 3,132
Posted By T.Rex
Hummmmm I understand your point. However, don't...

Hummmmm I understand your point.
However, don't you think that there are other ways for finding new stuff than using pure Math proof ? Is there a place for experimenting ? Years ago, before...
Forum: Miscellaneous Math 2015-09-08, 20:17
Replies: 27
Views: 3,132
Posted By T.Rex
:surrender Hummm Sometimes, I'm saying myself...

:surrender
Hummm Sometimes, I'm saying myself that I should go back to photography and forget Maths, where I was not so good even before I forgot so many things !
:surrender
Anyway, thanks for the...
Forum: Miscellaneous Math 2015-09-07, 21:53
Replies: 27
Views: 3,132
Posted By T.Rex
There are also pseudo primes for c=89, but not...

There are also pseudo primes for c=89, but not with 81, 87, 105, with the following bounds:
for(k=1,300,CEk2c(k,89,300)) :
133*2^262+89
221*2^291+89
266*2^261+89
Forum: Miscellaneous Math 2015-09-07, 18:42
Replies: 27
Views: 3,132
Posted By T.Rex
for(k=1,100,for(c=0,50,CEk2c(k,2*c+1,100))) :...

for(k=1,100,for(c=0,50,CEk2c(k,2*c+1,100))) : there are only 13 pseudoprimes out of 5588 numbers verifying the test; including 5575 primes: 0.23% of pseudoprimes. Out of a total of 125,000 numbers N...
Forum: Miscellaneous Math 2015-09-07, 17:32
Replies: 27
Views: 3,132
Posted By T.Rex
If we use the test as-is: ( if(s==sn && !...

If we use the test as-is: ( if(s==sn && ! isprime(N) ), it produces pseudoprimes, like: 1*2^3+1 or 98*2^79+17 .

for(k=1,100,for(c=0,50,CEk2c(k,2*c+1,100))) : produces 34 pseudoprimes.

But, if...
Forum: Miscellaneous Math 2015-09-06, 18:59
Replies: 27
Views: 3,132
Posted By T.Rex
About proving the sufficiency, I think that an...

About proving the sufficiency, I think that an issue (as I already said) is that s can be equal to sn before i==n-1 .
Finding s(n-1)==sn only after n-1 iterations and not before is important I...
Forum: Miscellaneous Math 2015-09-05, 19:41
Replies: 27
Views: 3,132
Posted By T.Rex
I should read again the documentation of...

I should read again the documentation of PARI/gp... ;) However, I'm now involved with porting Ruby and Python3, and then Go, on AIX, so I'm fed up reading language documentation. So, I know very...
Forum: Miscellaneous Math 2015-09-05, 10:42
Replies: 38
Views: 3,333
Posted By T.Rex
Yes. I've seen that recently. Robert Gerbicz used...

Yes. I've seen that recently. Robert Gerbicz used 3/2 mod N and Anton Vrba used 6, in 2008 October.
See: Gerbicz (https://trex58.files.wordpress.com/2009/01/wagstaffandfermat.pdf) and Vrba ...
Forum: Miscellaneous Math 2015-09-05, 10:30
Replies: 27
Views: 3,132
Posted By T.Rex
I do not think that this will speed up the...

I do not think that this will speed up the computation, since PARI goes in Stack overflow quickly. Modulo helps to keep s small.
Showing results 1 to 25 of 922

 
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