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Search: Posts Made By: T.Rex
Forum: Wagstaff PRP Search 2020-08-18, 22:15
Replies: 7
Views: 2,670
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: 2,670
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: 2,670
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: 1,039
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: 6,748
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: 1,583
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: 1,583
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: 1,583
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: 1,583
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: 1,583
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: 1,583
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: 1,583
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: 1,583
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: 1,583
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: 1,583
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: 1,693
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: 1,583
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.
Forum: Miscellaneous Math 2015-09-05, 10:26
Replies: 27
Views: 1,583
Posted By T.Rex
Ha ha ha ! No ! ;) I should have considered......

Ha ha ha ! No ! ;) I should have considered... but too busy with other stuff.
Forum: Miscellaneous Math 2015-09-04, 21:33
Replies: 27
Views: 1,583
Posted By T.Rex
Thanks to primus to have warned me about...

Thanks to primus to have warned me about Predrag's publication in StackExchange. :smile:
Forum: Miscellaneous Math 2015-09-04, 21:23
Replies: 27
Views: 1,583
Posted By T.Rex
Thumbs up Conjectured compositeness tests for N=k⋅2n±c by Predrag

Predrag (not sure he wants his name to appear since he published as "MathBot") has published a question in StackExchange...
Forum: Miscellaneous Math 2015-09-02, 18:53
Replies: 38
Views: 1,693
Posted By T.Rex
Here is what HC Williams and Mr Wagstaff had...

Here is what HC Williams and Mr Wagstaff had answered at the time I asked them some help:

Mr H.C. Williams :
"Because we cannot easily factor p-1 in your case, I am very doubtful that you will...
Forum: Miscellaneous Math 2015-09-02, 18:43
Replies: 38
Views: 1,693
Posted By T.Rex
Yes. Probably. However, there is no proof yet...

Yes. Probably. However, there is no proof yet that, if N is prime, it always verifies the property. It's good to know.
Moreover, he's close to the latest element of the sequence: 786441 . Greatest...
Forum: Miscellaneous Math 2015-09-02, 18:23
Replies: 38
Views: 1,693
Posted By T.Rex
Someone has posted a set of 4 much higher-level...

Someone has posted a set of 4 much higher-level conjectures k2^n ± c , which make use of Chebitchev functions that are connected to x^2-2 .
See: StackExchange...
Forum: Miscellaneous Math 2015-09-02, 18:13
Replies: 38
Views: 1,693
Posted By T.Rex
So, seed 6 seems to work too. Another Universal...

So, seed 6 seems to work too. Another Universal initial value.
Forum: Miscellaneous Math 2015-08-30, 21:50
Replies: 10
Views: 651
Posted By T.Rex
There is an issue with n==0 mod 3. Maybe 21...

There is an issue with n==0 mod 3. Maybe 21 should be used as seed instead of 13, which misses 2199.
More values are required.
Showing results 1 to 25 of 914

 
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