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Search: Posts Made By: paulunderwood
Forum: Math 2021-10-22, 11:21
Replies: 13
Views: 436
Posted By paulunderwood
I barely understand the necessity but would have...

I barely understand the necessity but would have to refer to the LL wiki page (https://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer_primality_test#Proof_of_correctness) for sufficiency.
Forum: Math 2021-10-22, 01:11
Replies: 13
Views: 436
Posted By paulunderwood
The LL test is performed with different hardware...

The LL test is performed with different hardware and different software for 100% confidence,
Forum: PrimeNet 2021-10-21, 12:50
Replies: 6
Views: 272
Posted By paulunderwood
Find out why you are getting Gerbicz errors. In...

Find out why you are getting Gerbicz errors. In the first place check your thermals with some temperature monitoring software. Other than this voltage and timings are crucial. What is the...
Forum: Miscellaneous Math 2021-10-20, 02:59
Replies: 29
Views: 3,217
Posted By paulunderwood
GMP code for test #3

I have coded up test #3 from the above paper.


// gcc -o prp prp.c -lgmp
// usages:-
// ./prp
// ./prp <integer>
// echo "print(<expression>)" | gp -q | ./prp
Forum: Math 2021-10-19, 11:50
Replies: 13
Views: 436
Posted By paulunderwood
We do a 3-PRP test because it uses a very...

We do a 3-PRP test because it uses a very reliable Gerbicz Error Correcting algorithm. If a Mersenne number is found to be 3-PRP we then proceed to an LL test. The chances of a 3-PRP not passing an...
Forum: Riesel Prime Search 2021-10-18, 22:55
Replies: 286
Views: 49,723
Posted By paulunderwood
Two birds with one stone

Congrats tp Ryan and Serge for the record Near-rep Digit / Palindrome prime 10^1888529 - 10^944264 - 1 (https://primes.utm.edu/primes/page.php?id=132851)
Forum: Riesel Prime Search 2021-10-18, 20:18
Replies: 438
Views: 83,812
Posted By paulunderwood
k=23

We would like to reserve k=23 from n=5,000,000 under "Underwood et al" :smile:
Forum: Math 2021-10-18, 14:11
Replies: 13
Views: 436
Posted By paulunderwood
Err, Nick, n^2^p would be n^2 mod Mp. Usually we...

Err, Nick, n^2^p would be n^2 mod Mp. Usually we use "a" not "n" and n=2^p-1.
Forum: Software 2021-10-18, 13:59
Replies: 508
Views: 99,966
Posted By paulunderwood
Thanks head -n1 Downloads/helper.ini | wc ...

Thanks

head -n1 Downloads/helper.ini | wc
1 1 21

Whereas 520461*2^55931+1 has 16+2 characters if Windows. Did you copy this number from the net?


cat -A...
Forum: Software 2021-10-18, 13:44
Replies: 508
Views: 99,966
Posted By paulunderwood
Please attach your helper file for inspection....

Please attach your helper file for inspection. :smile:

Use the forum's paperclip.
Forum: Software 2021-10-18, 11:08
Replies: 508
Views: 99,966
Posted By paulunderwood
If you have copy and pasted a number into the...

If you have copy and pasted a number into the helper file, especially from the web, it might have non-printable characters in it. Please attach the file "xyz".
Forum: Software 2021-10-18, 10:57
Replies: 508
Views: 99,966
Posted By paulunderwood
One thing to try: rename "xyz" to "helper" and...

One thing to try: rename "xyz" to "helper" and run with -hhelper
Forum: Software 2021-10-18, 10:39
Replies: 508
Views: 99,966
Posted By paulunderwood
Does xyz contain the word "numbers"?

Does xyz contain the word "numbers"?
Forum: PrimeNet 2021-10-16, 22:27
Replies: 108
Views: 26,252
Posted By paulunderwood
Work being done on my Odrod N2 running mlucas P-1...

Work being done on my Odrod N2 running mlucas P-1 has been poached - c105M. It is now switched off until next summer when it will be used for "small projects". The cost of electricity in the UK now...
Forum: Riesel Prime Search 2021-10-16, 17:54
Replies: 286
Views: 49,723
Posted By paulunderwood
Some numbers require proof attempts at increasing...

Some numbers require proof attempts at increasing sizes of FFT.
Forum: Programming 2021-10-15, 19:39
Replies: 41
Views: 1,203
Posted By paulunderwood
For lengthy numbers you might find this is better...

For lengthy numbers you might find this is better as there is no truncation:


ans=$(echo "print($d*$m)" | gp -q -f)
Forum: Miscellaneous Math 2021-10-14, 22:03
Replies: 2
Views: 137
Posted By paulunderwood
Semi-primes are being stubborn, but when I feed...

Semi-primes are being stubborn, but when I feed in Carmichael numbers counterexamples abound such as [n,a]=[19384289, 8494896]

This is yet another test that shows that X Frobenius tests with X...
Forum: Miscellaneous Math 2021-10-14, 01:56
Replies: 2
Views: 137
Posted By paulunderwood
I can save a few Selfridges by using the weaker...

I can save a few Selfridges by using the weaker form of Fermat's Little Theorem:

{
tst(n,a)=kronecker(a^2-4,n)==-1&&
gcd(a+4,n)==1&&
Mod(a-1,n)^n==a-1&&
Mod(a,n)^n==a&&
Mod(a+1,n)^n==a+1&&...
Forum: Hardware 2021-10-13, 20:21
Replies: 167
Views: 35,100
Posted By paulunderwood
https://thepihut.com/products/argon-one-m-2-raspbe...

https://thepihut.com/products/argon-one-m-2-raspberry-pi-4-case

Boot a pi from an M2 drive + 2 full size HDMI sockets
Forum: Miscellaneous Math 2021-10-13, 19:13
Replies: 2
Views: 137
Posted By paulunderwood
Talking Single Parameter Frobenius test -- 1+1+1+1+2 Selfridges

{
tst(n,a)=kronecker(a^2-4,n)==-1&&
gcd((a^3-a)*(a+4),n)==1&&
Mod(a-1,n)^(n-1)==1&&
Mod(a,n)^(n-1)==1&&
Mod(a+1,n)^(n-1)==1&&
Mod(a+4,n)^(n-1)==1&&
Mod(Mod(x+2,n),x^2-a*x+1)^(n+1)==2*a+5;}
...
Forum: Forum Feedback 2021-10-13, 14:34
Replies: 8
Views: 326
Posted By paulunderwood
I use hightlight then ctrl+shift+c to copy from a...

I use hightlight then ctrl+shift+c to copy from a terminal. Finally pasting with ctrl+v. To paste into a terminal use ctrl+shift+v. HTH :smile:
Forum: Riesel Prime Search 2021-10-08, 23:21
Replies: 706
Views: 76,862
Posted By paulunderwood
Here is another found with the Propper treatment:...

Here is another found with the Propper treatment:

https://primes.utm.edu/primes/page.php?id=132808 (1,935,350 digits)
Forum: Programming 2021-10-07, 02:16
Replies: 10
Views: 451
Posted By paulunderwood
I don't understand how it loses "n:". The first...

I don't understand how it loses "n:". The first line must be n and its value and not an empty line. It could be a better script, dropping "j".
Forum: Programming 2021-10-07, 01:18
Replies: 10
Views: 451
Posted By paulunderwood
#!/bin/bash readarray lines < $1 echo...

#!/bin/bash

readarray lines < $1
echo ${lines[0]}
i=1
j=${#lines[@]}
while ! [[ ${lines[$i]} =~ "skew" ]]; do
i=$(expr $i + 1)
echo ${lines[$(expr $j - $i )]}
done
Forum: Hardware 2021-10-06, 16:12
Replies: 22
Views: 4,332
Posted By paulunderwood
FWIW (not much) I implemented a base 3 Fermat PRP...

FWIW (not much) I implemented a base 3 Fermat PRP multi-limb test on my 32 bit Longan Nano. With a 16 bit model, a mult fits in in 32 bits with room for two 16 bit additions without overflow. I do...
Showing results 1 to 25 of 1000

 
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