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Forum: Miscellaneous Math 2021-02-24, 08:44
Replies: 72
Views: 3,512
Posted By mattprim
The proof of LL test to be all the time in the...

The proof of LL test to be all the time in the integer space is comparatively easy in special cases of the Mersenne exponent a it is for the Great (Last) Fermat Theorem. You can proceed like that...
Forum: Miscellaneous Math 2021-02-20, 15:25
Replies: 72
Views: 3,512
Posted By mattprim
I don't know precisely what you mean by Excel...

I don't know precisely what you mean by Excel programming. It is the table editor not the programming language. But if you mean the Microsoft Visual Basic:...
Forum: Miscellaneous Math 2021-02-19, 21:22
Replies: 72
Views: 3,512
Posted By mattprim
I am just proving it to you for one 3-2=1...

I am just proving it to you for one 3-2=1 iteration: 2^3-1=7 is the Mersenne prime and it is dividing s_1:

The prove of LL test not getting out of the integer number space is comparatively easy...
Forum: Miscellaneous Math 2021-02-19, 14:26
Replies: 72
Views: 3,512
Posted By mattprim
The prove of LL test not getting out of the...

The prove of LL test not getting out of the integer number space is comparatively easy for n=3 but it does not want go that way
easy for larger:

let s = x^2

Then let

s_1 = x^2*x^2 - x =...
Forum: Miscellaneous Math 2021-02-19, 11:33
Replies: 72
Views: 3,512
Posted By mattprim
Sorry, I am only mathematician with PhD trying to...

Sorry, I am only mathematician with PhD trying to do some research how to get 150 thousand dollars prize for 100 million digits prime. I actually believe there is some Fermat Last (Great) Theorem...
Forum: Miscellaneous Math 2021-02-19, 10:50
Replies: 72
Views: 3,512
Posted By mattprim
Here is the PariGP code which is running more...

Here is the PariGP code which is running more less the same fast (one night on 1.5 GHz) to check the same what which my Mathematica compiled code:

LL(p)={
my(m=Mod(4,1<<p-1));...
Forum: Miscellaneous Math 2021-02-19, 10:36
Replies: 72
Views: 3,512
Posted By mattprim
Here p is prime because it is Prime[p] i.e....

Here p is prime because it is Prime[p] i.e. p->Prime[p]. Mathematica function Prime[p] returns the p-th prime number i.e. Prime[1]=2, Prime[2]=3, Prime[3]=5 etc. I am not running it on 1572864 core...
Forum: Miscellaneous Math 2021-02-18, 11:56
Replies: 72
Views: 3,512
Posted By mattprim
I rewrote my code in Mathematica as Compiled and...

I rewrote my code in Mathematica as Compiled and Parallel. Mathematica is more like Interpreter than compiler and really very similar to Basic of computers like Sinclair Spectrum of Commodore 64 and...
Forum: Miscellaneous Math 2021-02-18, 10:10
Replies: 72
Views: 3,512
Posted By mattprim
... while using Compile with Parallelization ->...

... while using Compile with Parallelization -> True for LL routine makes it almost as fast as the PariGP:

a = Compile[{{p, _Integer}},
Module[{s, Mp}, Mp = 2^Prime[p] - 1; s = 4;
Do[s =...
Forum: Miscellaneous Math 2021-02-17, 13:33
Replies: 72
Views: 3,512
Posted By mattprim
This one is slightly faster checking only primes....

This one is slightly faster checking only primes. But on 1 GHz I got overnight only till 1979 anyway https://en.wikipedia.org/wiki/Mersenne_prime:

Do[Mp = 2^Prime[p] - 1;
s = 4;
Do[s =...
Forum: Miscellaneous Math 2021-02-17, 01:39
Replies: 72
Views: 3,512
Posted By mattprim
OK you probably mean that I should do If[s == 0,...

OK you probably mean that I should do If[s == 0, Print["PRIME"]; Print[p]] outside the loop but it looks by example that inside works too i.e. 0 can be faster. I actually never looked inside what is ...
Forum: Miscellaneous Math 2021-02-17, 01:17
Replies: 72
Views: 3,512
Posted By mattprim
Sorry I do not understand you here. By LL test I...

Sorry I do not understand you here. By LL test I mean what is defined here on wiki and called like that: https://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer_primality_test The code in gray field in...
Forum: Miscellaneous Math 2021-02-16, 09:33
Replies: 72
Views: 3,512
Posted By mattprim
You can find sever proofs of the LL test. Here is...

You can find sever proofs of the LL test. Here is for example the paper from Turkey: https://cs.uwaterloo.ca/journals/JIS/VOL21/Kucuksakalli/kucuk3.pdf with the references to other papers with...
Forum: Miscellaneous Math 2021-02-16, 01:23
Replies: 72
Views: 3,512
Posted By mattprim
OK. But the list is faster than the frequent...

OK. But the list is faster than the frequent calls.
Forum: Miscellaneous Math 2021-02-16, 00:50
Replies: 72
Views: 3,512
Posted By mattprim
Sorry I did not write this one by myself. Someone...

Sorry I did not write this one by myself. Someone sent it to me to show me how many Mersennes can be excluded fast. I think the loop over k here is not continuous but has quasi-random steps from the...
Forum: Miscellaneous Math 2021-02-16, 00:38
Replies: 72
Views: 3,512
Posted By mattprim
The LL test is so simple numerically that you can...

The LL test is so simple numerically that you can write your own code if you do not thrust mine. It is only more difficult to prove it works especially if you do not want to step out of the integer...
Forum: Miscellaneous Math 2021-02-13, 20:08
Replies: 72
Views: 3,512
Posted By mattprim
I suspected that even if I did not search through...

I suspected that even if I did not search through the documentation carefully. Actually at first without carefully reading the logs I thought that the option "Test" (my own guessed exponent) is...
Forum: Miscellaneous Math 2021-02-13, 17:59
Replies: 72
Views: 3,512
Posted By mattprim
I only wanted to know how Prime95 scales to...

I only wanted to know how Prime95 scales to "normal" numerical Physics Problems in the CPU time to write my own code. My piece of LL code works OK only is slower than Prime95 even in PariGP. It is...
Forum: Miscellaneous Math 2021-02-12, 19:49
Replies: 72
Views: 3,512
Posted By mattprim
I wanted to know how Prime95 works so did some...

I wanted to know how Prime95 works so did some research. Normally would write my own code with near infinite length binary arithmetics storying 1 and 0 in giant arrays: This for example that for...
Forum: Miscellaneous Math 2021-02-12, 19:45
Replies: 72
Views: 3,512
Posted By mattprim
Also PariGP LL test for n=41766037...

Also PariGP LL test for n=41766037 https://www.mersenne.ca/exponent/41766037 on above 1GHz Machine some 12 seconds per step at 240-th step and slowing down. Extimated check time 5800 days above 10...
Forum: Miscellaneous Math 2021-02-12, 09:31
Replies: 72
Views: 3,512
Posted By mattprim
Here is the proof of LL...

Here is the proof of LL https://rosettacode.org/wiki/Lucas-Lehmer_test test https://planetmath.org/proofoflucaslehmerprimalitytest . It's kind of tricky because it kicks out of the integer space to...
Forum: Miscellaneous Math 2021-02-12, 09:25
Replies: 72
Views: 3,512
Posted By mattprim
While PariGP in 70-ties ?: LL(p)={ ...

While PariGP in 70-ties ?: LL(p)={
my(m=Mod(4,1<<p-1));
for(i=3,p,m=m^2-2);
m==0
};
?
? search()={
print("2^2-1");
forprime(p=3,43112609,
if(LL(p), print("2^"p"-1"))
Forum: Miscellaneous Math 2021-02-11, 23:56
Replies: 72
Views: 3,512
Posted By mattprim
Lucas-Lehmer test in native Mathematica: p =...

Lucas-Lehmer test in native Mathematica:

p = 2976221;
s = 4;
Mp = 2^p - 1;
Do[s = Mod[(s*s - 2) , Mp];
If[s == 0, Print["PRIME"]], {i, 0, p - 2}];

puts me in top prime guys fast at least...
Forum: Miscellaneous Math 2021-02-11, 11:12
Replies: 72
Views: 3,512
Posted By mattprim
Mathematica has the native prime Number Theory...

Mathematica has the native prime Number Theory routines: PrimeQ, NextPrime, PrimePi etc. Just was mainly curious how PrimeQ[2^n-1] giving the answer if 2^n-1 is prime. You can actually link stuff...
Forum: Miscellaneous Math 2021-02-10, 17:06
Replies: 72
Views: 3,512
Posted By mattprim
Giant 2^58501120901-1 is divisible by...

Giant 2^58501120901-1 is divisible by 13384*2*58501120901+1 = 1565958004277969 (about 1Ghz x hour to test it knowing it from PariGP on the same Ghz)

PrimeQ[58501120901]

True
...
Showing results 1 to 25 of 29

 
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