mersenneforum.org  

Go Back   mersenneforum.org > Search Forums

Showing results 1 to 25 of 1000
Search took 0.28 seconds.
Search: Posts Made By: paulunderwood
Forum: And now for something completely different 2021-09-25, 18:36
Replies: 20
Views: 7,300
Posted By paulunderwood
:shock: :shock: :shock: :shock: Should that...

:shock: :shock: :shock: :shock:

Should that not be n=-1..2? And...

a=5606879602425*2^1290000-1 and d=33*2^2939063-5606879602425*2^1290000

So a-d is negative :ermm:

a+d = 33*2^2939063 - 1
Forum: Lounge 2021-09-24, 10:26
Replies: 20
Views: 352
Posted By paulunderwood
Cost of electricity -- compute for heat only

Here in the UK our electricity prices are about to go up by some 66% to in excess of £0,25 per kilowatt hour (plus £0.25 a day for the standing charge). This is a huge increase and is forcing me to...
Forum: And now for something completely different 2021-09-24, 00:50
Replies: 20
Views: 7,300
Posted By paulunderwood
:bow: This is huge! Surely it will top the second...

:bow: This is huge! Surely it will top the second table for top20 APs (https://primes.utm.edu/top20/page.php?id=14), with almost unassailable points. Nice ingenuity!
Forum: And now for something completely different 2021-09-21, 19:46
Replies: 13
Views: 360
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: 246
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: 246
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: 246
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: 273
Views: 47,284
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: 178
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: 178
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: 178
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: 178
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: 178
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: 24,803
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: 178
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: 178
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: 178
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: 273
Views: 47,284
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: 554
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: 273
Views: 47,284
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: 273
Views: 47,284
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: 100,219
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: 273
Views: 47,284
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: 322
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: 183
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.
Showing results 1 to 25 of 1000

 
All times are UTC. The time now is 19:21.


Sat Sep 25 19:21:01 UTC 2021 up 64 days, 13:50, 0 users, load averages: 1.08, 1.41, 1.39

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.