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Search: Posts Made By: paulunderwood
Forum: Hardware 2020-10-20, 17:26
Replies: 7
Views: 147
Posted By paulunderwood
Try running memtest86+. You might have one or...

Try running memtest86+. You might have one or more bad sticks of RAM.

Also install a temperature monitoring software.
Forum: Software 2020-10-18, 14:09
Replies: 22
Views: 2,746
Posted By paulunderwood
Arrow Speed up for N=2^n-c

Fermat's Little theorem states b^(N-1) == 1 mod N for prime N (and gcd(b,N)==1).

For N=2^n-c this means for b=3 that 3^(2^n-c-1) == 1 (mod 2^n-c). This can be rewritten as 3^(2^n) == 3^(c+1) (mod...
Forum: Miscellaneous Math 2020-10-17, 23:57
Replies: 18
Views: 717
Posted By paulunderwood
There is now a section on Gaussian primes, but...

There is now a section on Gaussian primes, but not mod n.

CRT: I find that quite difficult.

RSA: I have written that s or t may be chosen to be small for quick encoding or quick decoding...
Forum: Miscellaneous Math 2020-10-15, 15:48
Replies: 18
Views: 717
Posted By paulunderwood
I have tried to correct and clarify the text and...

I have tried to correct and clarify the text and arguments as Nick pointed out in the previous post. I have uploaded the latest version -- Oct 15th, 2020 -- to the original post....
Forum: Lounge 2020-10-14, 12:46
Replies: 7
Views: 1,424
Posted By paulunderwood
Prof. Chris Caldwell has offered up Yahoo!...

Prof. Chris Caldwell has offered up Yahoo! primenumbers group for administration and moderation. It is a useful comms channel for news about prime numbers and would be a pity to lose it. Is anybody...
Forum: Lounge 2020-10-14, 05:55
Replies: 7
Views: 1,424
Posted By paulunderwood
It is almost gone! It closes down completely Dec...

It is almost gone! It closes down completely Dec 15, 2020.

https://uk.help.yahoo.com/kb/groups/SLN35505.html

:sm88:
Forum: Software 2020-10-12, 17:35
Replies: 22
Views: 2,746
Posted By paulunderwood
I concur: testing a million digit number on an...

I concur: testing a million digit number on an i7:

v3.8.24: 0.749 ms/it
v3.8.21: 0.688 ms/it
Forum: Miscellaneous Math 2020-10-12, 05:33
Replies: 18
Views: 717
Posted By paulunderwood
Thank you very much for taking tome to read the...

Thank you very much for taking tome to read the text. I have made some changes to my local copy but will upload after more changes.
.
I mention it now in the both the paragraph on integers and when...
Forum: Miscellaneous Math 2020-10-11, 08:40
Replies: 18
Views: 717
Posted By paulunderwood
The man in the street with a little interest in...

The man in the street with a little interest in primes and testing :grin:

Please detail what the errors are so that I can fix them.
Forum: Miscellaneous Math 2020-10-10, 22:43
Replies: 18
Views: 717
Posted By paulunderwood
I have tidied up what I want write about "The...

I have tidied up what I want write about "The Fermatian Child".

I will refrain from reposting the paper until more input from folks.
Forum: Miscellaneous Math 2020-10-10, 22:40
Replies: 18
Views: 717
Posted By paulunderwood
I have read...

I have read https://en.wikipedia.org/wiki/Imaginary_unit What would you say I should write? i is fixed to be one of the two square roots of -1?
Forum: Miscellaneous Math 2020-10-10, 13:40
Replies: 18
Views: 717
Posted By paulunderwood
Prime Numbers Book

Enjoy and criticize. It ain't no C&P but might help some. :book:

After 20 downloads, I have made the changes to typos and Mersenne data. A new copy is now uploaded.

2 More downloads and I have...
Forum: Miscellaneous Math 2020-10-06, 00:38
Replies: 106
Views: 9,769
Posted By paulunderwood
A slight variation for x^2-y

Instead of using base x+1 choose to use base x+2. Then the test is, with any y=2^r-1, for non-square odd n:

find jacobi(y,n)==-1

then test

2^(n-1) == 1 (mod n)
y^((n-1)/2)==-1 (mod n)...
Forum: Soap Box 2020-10-05, 19:00
Replies: 13
Views: 295
Posted By paulunderwood
Happiness Is a Warm Gun. :bang: :bang:

Happiness Is a Warm Gun. :bang: :bang:
Forum: Software 2020-10-05, 17:30
Replies: 441
Sticky: Prime95 v30.3
Views: 25,406
Posted By paulunderwood
You could cancel your current Ubuntu LL...

You could cancel your current Ubuntu LL assignments through mersenne.org and request fresh PRP work.
Forum: Software 2020-10-04, 23:30
Replies: 6
Views: 217
Posted By paulunderwood
I don't know about 12 core chips running LLR, but...

I don't know about 12 core chips running LLR, but generally it makes sense to run 1 instance per chip or chiplet.
Forum: jvang 2020-10-04, 17:23
Replies: 19
Views: 557
Posted By paulunderwood
When you see iteration times of gpuOwl on a...

When you see iteration times of gpuOwl on a Radeon VII drop dramatically with memory overclocking without result degradation, you have to ask yourself "why not?". :smile:
Forum: Software 2020-10-03, 21:38
Replies: 6
Views: 217
Posted By paulunderwood
Running only one instance has all the cache too...

Running only one instance has all the cache too itself and will run quicker than running two instances where there will be contention for cache. On a 4c/8t box I run on instance with the -t4 option....
Forum: Number Theory Discussion Group 2020-10-03, 08:49
Replies: 4
Views: 263
Posted By paulunderwood
2^p - 1 == 0 mod Mp 2^p == 1 mod Mp k*2^p ==...

2^p - 1 == 0 mod Mp
2^p == 1 mod Mp
k*2^p == k mod Mp
That is k shifted to the left p-bits is equivalent to k.

If a and b each have no more than p bits then a*b is at most 2*p-1 bits, you can...
Forum: And now for something completely different 2020-10-02, 14:52
Replies: 5
Views: 314
Posted By paulunderwood
There may be some low hanging fruit in the masses...

There may be some low hanging fruit in the masses of data in factorDB, for you to practice some ECM/CHG/KP on. Perhaps some one else can give pointers to likely numbers
Forum: Proth Prime Search 2020-10-02, 07:11
Replies: 9
Views: 12,319
Posted By paulunderwood
Congrats to Ryan for the 17th largest known prime...

Congrats to Ryan for the 17th largest known prime 7*2^18233956 + 1 (https://primes.utm.edu/primes/page.php?id=131289) with 5,488,969 decimal digits,

:party:
Forum: Miscellaneous Math 2020-10-01, 20:52
Replies: 106
Views: 9,769
Posted By paulunderwood
Thumbs up Pari/GP took 32 hours to verify all "r" up to...

Pari/GP took 32 hours to verify all "r" up to n<10^12. GMP was just over 4 times faster. I could speed things a little by doing a base-2 Euler PRP test on the list of 2-PSP I am using, but I will...
Forum: And now for something completely different 2020-10-01, 18:17
Replies: 5
Views: 314
Posted By paulunderwood
There is the rub. Factorisation, usually ECM, of...

There is the rub. Factorisation, usually ECM, of larger factors of large numbers is CPU intensive. I have no figures on the CPU days required. I suggest you email Tom Wu...
Forum: And now for something completely different 2020-09-30, 18:21
Replies: 5
Views: 314
Posted By paulunderwood
Pari uses two functions: isprime() and...

Pari uses two functions: isprime() and ispseudoprime(). They are about the same for n<2^64. The latter is a probablistic test that since its conception in the '80's has no known counterexample -- I...
Forum: Miscellaneous Math 2020-09-28, 17:04
Replies: 106
Views: 9,769
Posted By paulunderwood
Question x^2-y test

I have devised another PRP for odd non-square n:

Let y = 2^r-1

Then seek

gcd(r-1,n-1)==1
kronecker(y,n)==-1

and test
Showing results 1 to 25 of 1000

 
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