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Forum: And now for something completely different 2021-09-21, 19:46
Replies: 13
Views: 314
Posted By paulunderwood
Mod 11 is used to get the check digit of ISBNs...

Mod 11 is used to get the check digit of ISBNs https://en.wikipedia.org/wiki/International_Standard_Book_Number#Check_digits
Forum: Lounge 2021-09-21, 02:02
Replies: 12
Views: 230
Posted By paulunderwood
You have a few options for heavy duty prime...

You have a few options for heavy duty prime number crunching. Number 1 is GIMPS, maybe you feel lucky and could find the next largest prime. Number 2 is PrimeGrid. They have plenty of sub-projects...
Forum: Lounge 2021-09-21, 01:37
Replies: 12
Views: 230
Posted By paulunderwood
The GPUs have 16GB each, enough to do two sets of...

The GPUs have 16GB each, enough to do two sets of P-1 factoring. So 16GB would be more than enough for the mainboaord. However on a more cores board it would be nice to have 64GB.

But I reiterate...
Forum: Lounge 2021-09-21, 01:16
Replies: 12
Views: 230
Posted By paulunderwood
Get a water cooled 32 core AMD with a couple of...

Get a water cooled 32 core AMD with a couple of secondhand AMD Radeon VII GPUs.

Alternatively buy a cheaper computer with sufficient RAM and 4 Radeon VIIs. (I see the secondhand market for R7's on...
Forum: Riesel Prime Search 2021-09-21, 00:39
Replies: 272
Views: 47,105
Posted By paulunderwood
The prof has been busy. He fixed the palindrome...

The prof has been busy. He fixed the palindrome length and puzzle-peter's arithmetic progression, which comes second on table two of https://primes.utm.edu/top20/page.php?id=14.

Hint: An AP9...
Forum: Miscellaneous Math 2021-09-19, 13:13
Replies: 7
Views: 171
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: 171
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: 171
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: 171
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: 171
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: 24,730
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: 171
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: 171
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: 171
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: 272
Views: 47,105
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: 10
Views: 517
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: 272
Views: 47,105
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: 272
Views: 47,105
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: 100,040
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: 272
Views: 47,105
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: 304
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: 169
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: 7,088
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: 92
Views: 3,663
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: 1,560
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...
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