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Forum: Miscellaneous Math 2021-09-19, 13:13
Replies: 7
Views: 145
Posted By paulunderwood
Different tack

Let the matrix A=[a,-1;1,0] with kronecker(a^2-4,n)==-1 && gcd(a^3-a,n)==1.

The latest test (LT) is A^n+t^n == (A+t)^n mod n.

with the following GCDs:-
gcd(t^3-t,n)==1
gcd(a+t,n)==1...
Forum: Miscellaneous Math 2021-09-19, 11:19
Replies: 7
Views: 145
Posted By paulunderwood
[n, t, t2]=[415681338623, 2106331569, 9028142873]...

[n, t, t2]=[415681338623, 2106331569, 9028142873] is a counterexample to the complex test (CT above). Hmm. I will try to find one for which gcd(a^3-a,n)==1. :grin:

Well that did not take long to...
Forum: Miscellaneous Math 2021-09-19, 06:18
Replies: 7
Views: 145
Posted By paulunderwood
[n, a, t, t2]=[8473, 2043, 140, 1252] gives a...

[n, a, t, t2]=[8473, 2043, 140, 1252] gives a counterexample, but fear not, I have added gcd(a+t,n)==1 (to GT()) to stop degeneration of the determinant t*(t+a)+1 into unity, and gcd(t*a+1,n)==1 for...
Forum: Miscellaneous Math 2021-09-19, 01:05
Replies: 7
Views: 145
Posted By paulunderwood
For the 1+2+2 Selfridges tst_2_4(n,a) it will be...

For the 1+2+2 Selfridges tst_2_4(n,a) it will be nice to write some GMP code against Feitsma's list of Fermat 2-PRPs n < 2^64 -- I will have to see how far I can get. :smile:

<placeholder for code>
Forum: Miscellaneous Math 2021-09-19, 00:07
Replies: 7
Views: 145
Posted By paulunderwood
If t = 2 and t2 = 3 then the above general test...

If t = 2 and t2 = 3 then the above general test is:


{
tst_2_3(n,a)=
kronecker(a^2-4,n)==-1&&
gcd(210,n)==1&&
gcd(a+4,n)==1&&
gcd(a+6,n)==1&&
Mod(2,n)^(n-1)==1&&
Forum: And now for something completely different 2021-09-18, 20:02
Replies: 80
Views: 24,643
Posted By paulunderwood
Congrats to Facq, Asuncion and Allombert for...

Congrats to Facq, Asuncion and Allombert for breaking the ECPP 30k barrier with the proof of U(148091) (https://primes.utm.edu/primes/page.php?id=132721) -- Fibonacci Number with 30,949 decimal...
Forum: Miscellaneous Math 2021-09-18, 14:54
Replies: 7
Views: 145
Posted By paulunderwood
With the counterexample [n, a, t, t2,...

With the counterexample [n, a, t, t2, gcd((t*t2)^2-1,n), gcd(t^2-t2^2,n)] = [5983, 5514, 5512, 5982, 1, 1] it is advisable to take the above GCD giving a non-degenerative Fermat PRP-t test. For this...
Forum: Miscellaneous Math 2021-09-18, 08:37
Replies: 7
Views: 145
Posted By paulunderwood
[Side note: gcd(t^3-t,n)==1 might not be required...

[Side note: gcd(t^3-t,n)==1 might not be required in the above tests.]

I'll try to convey my thinking here.

Let A be the matrix [a,-1;1,0] and its characteristic function be X(A).

Note that...
Forum: Miscellaneous Math 2021-09-18, 04:44
Replies: 7
Views: 145
Posted By paulunderwood
Talking Singleton / Complex / General Tests -- Trinomiality Preservation

Singleton Case - 2 Selfridges
If n = 3 mod 4 then (x+2)^(n+1)==5 (mod n, x^2+1), which has been verified to 2^50.

Complex Case - Double Test - Two Parameters
Only for n==3 mod 4.
Let CT(t,n) =...
Forum: Riesel Prime Search 2021-09-15, 11:19
Replies: 267
Views: 46,780
Posted By paulunderwood
No they are not :no: Reversing the digits does...

No they are not :no: Reversing the digits does not give the same number.

https://primes.utm.edu/primes/page.php?id=132715 is a palindrome. Congrats Serge and Ryan.

UTM's Prime Pages parser...
Forum: Software 2021-09-15, 10:53
Replies: 3
Views: 322
Posted By paulunderwood
I don't know about efforts to put GWNUM in GMP,...

I don't know about efforts to put GWNUM in GMP, but you could write your own functions like

gw_mul( mpz_t r, mpz_t a, mpz_t b ) {
...
}

:smile:
Forum: Riesel Prime Search 2021-09-14, 21:01
Replies: 267
Views: 46,780
Posted By paulunderwood
I am looking forward to its revelation. The...

I am looking forward to its revelation. The largest palindrome before this one had 490,001 digits. So 1,234,567 digits is quite amazing considering its crunching is done with generic modular...
Forum: Riesel Prime Search 2021-09-12, 17:20
Replies: 267
Views: 46,780
Posted By paulunderwood
Congrats to Marc Wiseler and PrimeGrid for the...

Congrats to Marc Wiseler and PrimeGrid for the "321" prime 3*2^17748034-1 (https://primes.utm.edu/primes/page.php?id=132678) (5,342,692 decimal digits) ranked as the 18th largest known prime.
...
Forum: XYYXF Project 2021-09-11, 12:43
Replies: 477
Views: 99,724
Posted By paulunderwood
Although it good to us another library, for...

Although it good to us another library, for numbers of this size you can use the -tc switch of PFGW to get a combined Fermat+Lucas result, which is much quicker.

Congrats for such a huge find.
Forum: Riesel Prime Search 2021-09-11, 08:21
Replies: 267
Views: 46,780
Posted By paulunderwood
Congrats to Serge and Ryan for the two smallest...

Congrats to Serge and Ryan for the two smallest known Mega primes, prove with CHG at 28.7% factored of N+1

10^999999 - 1022306*10^287000 - 1 (https://primes.utm.edu/primes/page.php?id=132705)
...
Forum: Software 2021-09-09, 11:39
Replies: 7
Views: 280
Posted By paulunderwood
That syntax would clash with: You...

That syntax would clash with:



You could always write a GMP program to do this, or even PARI/GP
Forum: Information & Answers 2021-09-09, 11:31
Replies: 3
Views: 146
Posted By paulunderwood
The 64 core TR comprises of 8 chiplets and so it...

The 64 core TR comprises of 8 chiplets and so it is best to run 8 workers at the current wavefront of GIMPS. Forget using Hyper Threading -- only real cores count.
Forum: And now for something completely different 2021-09-07, 10:43
Replies: 11
Views: 7,058
Posted By paulunderwood
Congrats, Peter, for this AP-6. I am looking...

Congrats, Peter, for this AP-6. I am looking forward to your submissions to the UTM top20 and JK Andersen's list.

:party:
Forum: Factoring 2021-09-05, 15:59
Replies: 91
Views: 3,376
Posted By paulunderwood
Did you install with YaST the dev package of...

Did you install with YaST the dev package of libstdc++?
Forum: Puzzles 2021-09-05, 14:24
Replies: 58
Views: 1,491
Posted By paulunderwood
Suppose the farmer has to enclose the roof with...

Suppose the farmer has to enclose the roof with part of the 200m roll of fencing and that roll is 1m wide (and that the wall is 50m high). He may, by doing some simple wood work, run two or more...
Forum: Mlucas 2021-09-05, 02:47
Replies: 7
Views: 540
Posted By paulunderwood
factor found on a73

Yay, I found my first factor using the a73 of my Odroid N2: Found 77-digit factor in Stage 2: 126440940410782170073559 (of M105592247)

Clocks for stage 2 have gone from 00:25:14 (v20) to 00:23:39...
Forum: Factoring 2021-09-05, 02:24
Replies: 91
Views: 3,376
Posted By paulunderwood
Use YaST to search for the dev file of libstdc++...

Use YaST to search for the dev file of libstdc++ and install it (and its dependencies), and then link with -lstdc++
Forum: Factoring 2021-09-04, 17:20
Replies: 91
Views: 3,376
Posted By paulunderwood
Did you install through Yast or a direct download...

Did you install through Yast or a direct download from nVidia?
Forum: Factoring 2021-09-04, 16:58
Replies: 91
Views: 3,376
Posted By paulunderwood
Following this solution...

Following this solution (https://askubuntu.com/questions/1095825/what-does-modprobe-blacklist-nouveau-do) (although Ubuntu)



reboot.

run lsmod | grep nvidia

HTH
Forum: Software 2021-08-30, 19:20
Replies: 3
Views: 195
Posted By paulunderwood
Search for embedding C in Python :google:

Search for embedding C in Python

:google:
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