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Search: Posts Made By: paulunderwood
Forum: Miscellaneous Math 2022-08-19, 04:47
Replies: 6
Views: 283
Posted By paulunderwood
A small observation: If a number n==3 mod 4 is...

A small observation: If a number n==3 mod 4 is Fermat 2-PRP then 2^(n-1)==1 mod n. If z is the multiplicative order of 2 mod n, then z divides n-1. Also (x+2^z) == x+1 mod n. Furthermore, (x+1)^(n+1)...
Forum: Miscellaneous Math 2022-08-18, 15:26
Replies: 6
Views: 283
Posted By paulunderwood
Recap: I am testing: Fermat 2-prp and...

Recap: I am testing: Fermat 2-prp and (x+2^r)^(n+1)==4^r+1 where gcd(r,n-1)==1, and have reached n<4*10^14 without counterexample.

Now, writing a=lift(Mod(2,n)^r) the Lucas part can be written as...
Forum: And now for something completely different 2022-08-07, 17:52
Replies: 188
Views: 14,404
Posted By paulunderwood
FactorDB has verified it. Now The Prime Pages...

FactorDB has verified it. Now The Prime Pages awaits your submission under: Generalized Lucas number, Wagstaff, ECPP :smile:
Forum: Linux 2022-08-03, 22:31
Replies: 10
Views: 680
Posted By paulunderwood
I have never used screen before and am just...

I have never used screen before and am just playing around with it now. It seems you want sudo crontab -e (or root's account) and enter there @reboot su math-user -c "cd /your/path && screen...
Forum: And now for something completely different 2022-08-02, 23:31
Replies: 49
Views: 10,682
Posted By paulunderwood
Nice one :tu:

Nice one :tu:
Forum: Linux 2022-08-02, 11:26
Replies: 10
Views: 680
Posted By paulunderwood
I see this as two problems: Firstly getting...

I see this as two problems: Firstly getting something to run at boot and secondly getting something to run when logging in.

For the first use @reboot su math-user -c "X" (in sudo crontab -e) where...
Forum: Linux 2022-07-31, 18:51
Replies: 10
Views: 680
Posted By paulunderwood
I think you need to use screen as a @reboot cron...

I think you need to use screen as a @reboot cron job.

Details somebody please.
Forum: Chess 2022-07-24, 20:30
Replies: 5
Views: 357
Posted By paulunderwood
First Law of Robotics broken

The first law of robotics (https://en.wikipedia.org/wiki/Three_Laws_of_Robotics) has been broken. A 7 year boy has been injured playing chess...
Forum: sweety439 2022-07-22, 21:39
Replies: 13
Views: 556
Posted By paulunderwood
Can't you stop asking all and sundry "Can you...

Can't you stop asking all and sundry "Can you run...." or "Please factor...". If you persist, we mods will create a repository of such requests. You have hereby been warned.
Forum: Riesel Prime Search 2022-07-22, 04:12
Replies: 1,984
Views: 249,546
Posted By paulunderwood
9473*2^4543680-1...

9473*2^4543680-1 (https://primes.utm.edu/primes/page.php?id=134201) (1367788 digits) found Vincent Diepeveen
Forum: Proth Prime Search 2022-07-21, 14:42
Replies: 1
Views: 248
Posted By paulunderwood
Cool 6 million digits prime!

Congrats to Ryan for 7*2^20267500 + 1 (https://primes.utm.edu/primes/page.php?id=134192) with 6,101,127 digits and entrance rank 17 in top5000.

:banana: :banana: :banana: :banana: :banana:...
Forum: science_man_88 2022-07-20, 20:46
Replies: 2
Views: 232
Posted By paulunderwood
WB sm88. I never know if to use my or local,...

WB sm88.

I never know if to use my or local, but your code can be made better by:

div(n,x)=local(tz=10^znorder(Mod(10,x)));if(n<=tz,return(n),return(n%tz+div(floor(n/tz),x)))

I think znorder...
Forum: Miscellaneous Math 2022-07-19, 18:03
Replies: 6
Views: 283
Posted By paulunderwood
Let z=znorder(Mod(2,n)). Then...

Let z=znorder(Mod(2,n)).

Then [2^(z-r),-1;1,2^(z-r)]^(n+1) == 4^(z-r)+1 == (4^z+4^r)/(4^r) == (1+4^r)/4^r all mod n

So 2^(r*(n+1))*[2^-r,-1;1,2^-r]^(n+1) = (1+4^r)*2^(r*(n-1)) mod n

Or...
Forum: Miscellaneous Math 2022-07-18, 23:48
Replies: 6
Views: 283
Posted By paulunderwood
Rather than computing gcd(a^3-a,n)==1 I think...

Rather than computing gcd(a^3-a,n)==1 I think gcd(r,(n-1)/2)==1 is better. Certainly verification testing is quicker (both over znorder).

Note n divides 2^(n-1)-1.

gcd(a^2-1,n)==1 ==>...
Forum: Miscellaneous Math 2022-07-18, 18:26
Replies: 6
Views: 283
Posted By paulunderwood
Finding a counterexample to this looks hopeless....

Finding a counterexample to this looks hopeless. Before my computer crashed under the heat of the day, it had reached 4e11. I suspect a counterexample at maybe 25 digits or more. Very much more for...
Forum: Miscellaneous Math 2022-07-17, 20:34
Replies: 6
Views: 283
Posted By paulunderwood
Answer: [n, a]=[79786523, 1056446] Now for a...

Answer: [n, a]=[79786523, 1056446]

Now for a harder problem: Let a = 2^r, so that the test becomes:

{tst(n,r)=local(a=lift(Mod(2,n)^r));
n%4==3&&
gcd(a^3-a,n)==1&&
Mod(2,n)^(n-1)==1&&...
Forum: Miscellaneous Math 2022-07-17, 16:29
Replies: 6
Views: 283
Posted By paulunderwood
3 mod 4 with free parameter

Consider [a,-1;1,a] = 2*a + [-a,-1;1,-a] where M=[a,-1;1,a] has the character x^2-2*a*x+a^2+1 and its discriminant = -1. Solving the character gives x=a+-sqrt(-1), leading to a test:
...
Forum: And now for something completely different 2022-07-17, 08:07
Replies: 49
Views: 10,682
Posted By paulunderwood
I am now certifying revnumbpart(100031088) on a...

I am now certifying revnumbpart(100031088) on a slow computer.
Forum: Information & Answers 2022-07-16, 16:51
Replies: 16
Views: 510
Posted By paulunderwood
Install lm-sensors, and run watch sensors and...

Install lm-sensors, and run watch sensors and report back the respective temperatures.
Forum: Information & Answers 2022-07-16, 15:24
Replies: 16
Views: 510
Posted By paulunderwood
It is not unknown that sometimes a CPU needs...

It is not unknown that sometimes a CPU needs reseating. This will also ensure you have perfect contact between the CPU and the heatsink, separted by the thinnest layer of paste when you reinstall the...
Forum: And now for something completely different 2022-07-16, 07:01
Replies: 49
Views: 10,682
Posted By paulunderwood
Using the following function to reverse the...

Using the following function to reverse the digits of number of partitions:

revnumbpart(n)=V=digits(numbpart(n));a=0;for(k=1,#V,a+=V[k]*10^(k-1));a;

I get in seconds:
...
Forum: sweety439 2022-07-15, 10:27
Replies: 13
Views: 556
Posted By paulunderwood
Yet another thread hijacked with the same...

Yet another thread hijacked with the same off-topic ramblings from sweety. Sweety, please confine your "studies" to your blog :rant:
Forum: And now for something completely different 2022-07-14, 06:57
Replies: 49
Views: 10,682
Posted By paulunderwood
You'll be enlightened soon. CM is is a joy with...

You'll be enlightened soon. CM is is a joy with its MPI abilities. Like you say, a prime a day. It is so much fun in comparison to running Primo. Chuck is cutting back to one every 10 days :smile:
Forum: And now for something completely different 2022-07-13, 19:33
Replies: 49
Views: 10,682
Posted By paulunderwood
After almost filling the top20 Partitions primes...

After almost filling the top20 Partitions primes table with numbers above 13k digits, with our E6 prover code, and starting to eat our own tail, we notice Serge's submissions at 14k digits and so we...
Forum: Soap Box 2022-07-13, 19:04
Replies: 7
Views: 370
Posted By paulunderwood
Herr Gel has stiff competition from those willing...

Herr Gel has stiff competition from those willing to spend some, mostly uncosted, £300,000,000,000 on tax cuts at the expense of services (like nurses pay) -- a how-much-tax-I-will-cut race.
Showing results 1 to 25 of 1000

 
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