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Forum: storm5510 2022-07-03, 15:13
Replies: 5
Views: 97
Posted By paulunderwood
PRP means Probable Prime. That probability might...

PRP means Probable Prime. That probability might be 99.999999999999% but it is not 100%. Some numbers that are 3-PRP are not prime. For example 91 = 7*13. That is 91 is a base 3 Fermat pseudoprime.
...
Forum: XYYXF Project 2022-07-03, 11:12
Replies: 568
Views: 125,742
Posted By paulunderwood
Congrats to frmky for the proof of...

Congrats to frmky for the proof of 3^78296+78296^3 (https://primes.utm.edu/primes/page.php?id=134104) with 37,357 decimal digits :banana:
Forum: And now for something completely different 2022-07-01, 10:55
Replies: 184
Views: 11,491
Posted By paulunderwood
In stage one is says "Step [X]: xxxxx bits". The...

In stage one is says "Step [X]: xxxxx bits". The number of bits is also printed in stage 2.

A good start would be to learn about the arithmetic of rational points on elliptic curves:...
Forum: And now for something completely different 2022-07-01, 06:19
Replies: 184
Views: 11,491
Posted By paulunderwood
I do it like this. If the current number of bits...

I do it like this. If the current number of bits is for example 3/4 of the starting number of bits, then it has left (3/4)^4 == 3^4/4^4 = 81/256 about 1/3 to go. Note also each step is about 70...
Forum: And now for something completely different 2022-06-30, 19:02
Replies: 184
Views: 11,491
Posted By paulunderwood
The factors of N+-1 don't matter for a test...

The factors of N+-1 don't matter for a test number. I could have equally said 2^4253-1.
Forum: XYYXF Project 2022-06-30, 17:13
Replies: 57
Views: 16,544
Posted By paulunderwood
sweety439 fails to mention the 30% of KP and...

sweety439 fails to mention the 30% of KP and 25%+epsilon of CGH. Also, Primo is currently old hat and people are using FastECPP/CM.
Forum: XYYXF Project 2022-06-30, 17:07
Replies: 57
Views: 16,544
Posted By paulunderwood
You understood correctly: (3892,765) is shorthand...

You understood correctly: (3892,765) is shorthand notation herein for 3892^765+765^3892.
Forum: XYYXF Project 2022-06-30, 16:47
Replies: 57
Views: 16,544
Posted By paulunderwood
This is prime hunting 101. The number 91 is 3-PRP...

This is prime hunting 101. The number 91 is 3-PRP yet factors into 7*13. To be 100% sure of primality we need to follow a method that actually proves the number prime -- in this case ECPP is used for...
Forum: And now for something completely different 2022-06-30, 12:24
Replies: 184
Views: 11,491
Posted By paulunderwood
Those are accumulative times. Each step is...

Those are accumulative times. Each step is quicker than the last. It runs at O(log(n)^4) meaning a number twice in length takes 16 times as long to compute. So as each of the two stages finish it...
Forum: XYYXF Project 2022-06-28, 13:56
Replies: 568
Views: 125,742
Posted By paulunderwood
mtsieve...

mtsieve (https://sourceforge.net/projects/mtsieve/) + OpenPFGW (https://sourceforge.net/projects/openpfgw/) is my guess :smile:
Forum: XYYXF Project 2022-06-26, 17:31
Replies: 568
Views: 125,742
Posted By paulunderwood
http://factordb.com/index.php?showid=1100000003609...

http://factordb.com/index.php?showid=1100000003609777732
Forum: Soap Box 2022-06-25, 00:14
Replies: 161
Views: 12,400
Posted By paulunderwood
bzVHjg3AqIQ

bzVHjg3AqIQ
Forum: Hardware 2022-06-24, 23:33
Replies: 248
Views: 51,164
Posted By paulunderwood
I understand the distraction to your key skills...

I understand the distraction to your key skills of coding but there are a few more things you should try with the PSU+Motherboard+CPU:

Step 0. Make sure the pump and radiator fans are plugged into...
Forum: Miscellaneous Math 2022-06-24, 22:28
Replies: 32
Views: 793
Posted By paulunderwood
:lol: For my next tricks, I have forgotten how to...

:lol: For my next tricks, I have forgotten how to prove pi is transcendental, the proof of Prime Number Theorem and have never quite figured out the proof of Riemann's Hypothesis.
Forum: Miscellaneous Math 2022-06-24, 21:46
Replies: 32
Views: 793
Posted By paulunderwood
I have forgotten how to prove e is...

I have forgotten how to prove e is transcendental. Intuitively, it cannot be written algabraically. Without me referring to my Spivak book, can you explain how it is proven transcendental? e^11 is...
Forum: Miscellaneous Math 2022-06-24, 21:22
Replies: 32
Views: 793
Posted By paulunderwood
I think it does converge. The terms approach 0 as...

I think it does converge. The terms approach 0 as n goes to infinity. I can quite make subsets of terms be bounded and making the subset sum less then some bound which clearly is by experimentation...
Forum: Software 2022-06-24, 14:04
Replies: 5
Views: 222
Posted By paulunderwood
Not really. I can run with (P,1) with min P:...

Not really. I can run with (P,1) with min P: Jacobi(P^2-4,n)==-1. Will that do for you sir?

Here are the results as they come in:


echo 'print((57*11^62668-7)/10)' | gp -q |...
Forum: Software 2022-06-24, 13:28
Replies: 5
Views: 222
Posted By paulunderwood
No. PFGW does not run a strong Lucas PRP test. It...

No. PFGW does not run a strong Lucas PRP test. It could if you altered the source code. If you really want to strong Lucas test these numbers you could run the GMP program...
Forum: And now for something completely different 2022-06-24, 06:03
Replies: 164
Views: 36,290
Posted By paulunderwood
AFAIK factorDB lacks the ability to verify both...

AFAIK factorDB lacks the ability to verify both KP and CHG proofs.
Forum: Miscellaneous Math 2022-06-24, 05:57
Replies: 32
Views: 793
Posted By paulunderwood
I think you meant 11^N/(N!). :smile:

I think you meant 11^N/(N!). :smile:
Forum: MattcAnderson 2022-06-23, 20:34
Replies: 5
Views: 120
Posted By paulunderwood
10^2^k+1 is a Generalized Fermat Number. There...

10^2^k+1 is a Generalized Fermat Number. There are very few Fermat Numbers that are prime. There will be fewer base 10 GFN primes is my guess.
Forum: And now for something completely different 2022-06-23, 11:40
Replies: 164
Views: 36,290
Posted By paulunderwood
It is ranked now. Try adding a comment.

It is ranked now. Try adding a comment.
Forum: And now for something completely different 2022-06-23, 11:17
Replies: 164
Views: 36,290
Posted By paulunderwood
The database re-ranks primes every 30 mins.

The database re-ranks primes every 30 mins.
Forum: And now for something completely different 2022-06-22, 19:19
Replies: 184
Views: 11,491
Posted By paulunderwood
The ultimate Ver_6 has been uploaded to post 148...

The ultimate Ver_6 has been uploaded to post 148 (https://mersenneforum.org/showpost.php?p=606916&postcount=148). It uses functions and a neat piece of code to calculate odd d for n-1=d*2^r thanks to...
Forum: And now for something completely different 2022-06-22, 18:58
Replies: 164
Views: 36,290
Posted By paulunderwood
It's a bit involved. I think you have enter the...

It's a bit involved. I think you have enter the whole number as a "blob" and give it the label: "tau(47^4176)". However if it does not have more than 26,709 digits as of today it is inadmissible to...
Showing results 1 to 25 of 1000

 
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