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Forum: Prime Gap Searches 2020-09-30, 04:38
Replies: 148
Sticky: Prime Gap News
Views: 21,133
Posted By danaj
:lol:All my computers have been packed away...

:lol:All my computers have been packed away turned off for the last 1.5 years. Maybe when Covid-19 settles down and I return to the USA I'll get them going again. I feel bad for not keeping up with...
Forum: Prime Gap Searches 2020-09-11, 02:15
Replies: 82
Views: 9,364
Posted By danaj
Arxiv: "Primes in short intervals: Heuristics and...

Arxiv: "Primes in short intervals: Heuristics and calculations (https://arxiv.org/abs/2009.05000)" by Granville and Lumley, 10 Sep 2020. Interesting.
Forum: Miscellaneous Math 2020-09-01, 11:59
Replies: 10
Views: 780
Posted By danaj
I found the paper by Padró and Sáez (2002) (paper...

I found the paper by Padró and Sáez (2002) (paper (https://www.sciencedirect.com/science/article/pii/S0893965902000319)) to work well for cube roots. It shows an explicit modification to...
Forum: Computer Science & Computational Number Theory 2020-08-30, 11:31
Replies: 32
Views: 9,539
Posted By danaj
Fantastic! I've been following the git repo...

Fantastic! I've been following the git repo watching the continuing improvements to the code.
Forum: Factoring 2020-06-10, 04:30
Replies: 13
Views: 1,470
Posted By danaj
https://en.wikipedia.org/wiki/Modulo_operation ...

https://en.wikipedia.org/wiki/Modulo_operation

For even more interesting reading. It's implementation defined in C (this bit me a few times while doing printer firmware, because our HP/UX...
Forum: Computer Science & Computational Number Theory 2020-05-24, 12:35
Replies: 32
Views: 9,539
Posted By danaj
:smile: :smile: :smile: :smile:

:smile: :smile: :smile: :smile:
Forum: Prime Gap Searches 2019-05-03, 11:28
Replies: 21
Views: 1,397
Posted By danaj
I ran to 10^20 last night without finding any. I...

I ran to 10^20 last night without finding any. I just spent a few minutes and tested the other three types to 10^17 without finding any.

I did a simple look at the 3rd type of 11 twins to 10^19...
Forum: Prime Gap Searches 2019-05-01, 16:31
Replies: 21
Views: 1,397
Posted By danaj
$ perl -Mntheory=:all -E...

$ perl -Mntheory=:all -E 'prime_set_config(verbose=>2); say for sieve_prime_cluster(0,1e14,2,6,8,18,20,30,32,36,38,48,50,60,62,78,80);'
cluster sieve found 1 residues mod 30
cluster sieve found 1...
Forum: Prime Gap Searches 2019-05-01, 16:28
Replies: 21
Views: 1,397
Posted By danaj
For your second example, it takes 40 seconds to...

For your second example, it takes 40 seconds to test to 10^14 using sieve_prime_cluster in serial on my macbook. Use the ktuplet-threads.pl example script to run in parallel.

29
2595051759329...
Forum: Programming 2019-04-24, 13:07
Replies: 7
Views: 4,954
Posted By danaj
It is about time. I know WraithX submitted his...

It is about time. I know WraithX submitted his code to them years ago. IIRC it is a slower than mine, though in a nice neat library. I'd like to see either a standard Selfridge strong Lucas test,...
Forum: Factoring 2019-04-03, 15:28
Replies: 55
Views: 2,944
Posted By danaj
I also got from the paper that SM was not the end...

I also got from the paper that SM was not the end goal, and I wasn't commenting on that. I think RM is certainly interesting and non-obvious.

Mainly since we've had discussions on this forum of...
Forum: Factoring 2019-04-02, 21:13
Replies: 55
Views: 2,944
Posted By danaj
The SM method looks to be Hart's OLF (as alluded...

The SM method looks to be Hart's OLF (as alluded to in the text) using a multiplier. Translating the "Simple Multiplication algorithm" from pseudocode into C becomes exactly my existing code for...
Forum: Forum Feedback 2019-03-27, 17:35
Replies: 17
Views: 1,870
Posted By danaj
Forum: Miscellaneous Math 2019-03-21, 16:36
Replies: 5
Views: 253
Posted By danaj
Good point. The sources don't even include a...

Good point. The sources don't even include a range for a in the theorems so they side-step it that way. Only when one has to actually go implement something to *find* a suitable value does this...
Forum: Puzzles 2019-03-21, 16:33
Replies: 215
Views: 29,780
Posted By danaj
Using GMP, assuming it all fits in memory and GMP...

Using GMP, assuming it all fits in memory and GMP scales fine, it's only 1.8 billion years to finish BPSW.

My single threaded Primo calculation came out to only exp( 4.01 *...
Forum: Miscellaneous Math 2019-03-21, 16:12
Replies: 5
Views: 253
Posted By danaj
Page 173-174 of Crandall and Pomerance discusses...

Page 173-174 of Crandall and Pomerance discusses this particular test. The theorem itself has no restrictions on a. Their remark is that one chooses random 1 <= a <= n-1. I'm not sure why one...
Forum: Miscellaneous Math 2019-03-10, 03:39
Replies: 5
Views: 337
Posted By danaj
For the case of base 2, you can go even one step...

For the case of base 2, you can go even one step further. It is even more discriminating than the Fermat and Euler tests, though less than a full strong pseudoprime (i.e. Miller-Rabin) test. To my...
Forum: Twin Prime Search 2019-03-09, 14:40
Replies: 8
Views: 2,585
Posted By danaj
Sigh, I now realize this was a test for the OP to...

Sigh, I now realize this was a test for the OP to show how well his method works. Well, ok um you can use the rest of this as a comparison I guess.




10^1000 + 9705091 is the smaller of the...
Forum: Prime Gap Searches 2019-03-09, 01:16
Replies: 23
Views: 1,504
Posted By danaj
Also see A055381 (https://oeis.org/A055381) and...

Also see A055381 (https://oeis.org/A055381) and A055382 (https://oeis.org/A055382). It seems they've already found the first ones up to 12-interprime.

Apparently there was a distributed project...
Forum: Prime Gap Searches 2019-03-08, 22:13
Replies: 23
Views: 1,504
Posted By danaj
Some simple transforms of Robert's code give a...

Some simple transforms of Robert's code give a ~2x speedup, or about 22e9/hour on a single-thread Macbook.

But then perhaps we notice that oneminus and oneplus are just the last and current prime...
Forum: Lounge 2019-03-04, 04:58
Replies: 108
Views: 7,760
Posted By danaj
It's interesting that a common list of long place...

It's interesting that a common list of long place (https://www.worldatlas.com/articles/the-10-longest-place-names-in-the-world.html) names claims...
Forum: Software 2019-03-02, 05:39
Replies: 19
Views: 1,492
Posted By danaj
Mathematica is a nice general purpose program. ...

Mathematica is a nice general purpose program. But it really isn't the fastest at a lot of things. Good GMP code or specific programs for operations can often be quite a bit faster. As others have...
Forum: Prime Gap Searches 2019-02-27, 21:54
Replies: 42
Views: 5,085
Posted By danaj
+20 points! If only the modern-day...

+20 points!

If only the modern-day Inquisition would stop changing the thread titles.
Forum: Other Mathematical Topics 2019-02-19, 17:13
Replies: 24
Views: 2,434
Posted By danaj
Dudley's paper "Formulas for Primes...

Dudley's paper "Formulas for Primes (https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/formulas-for-primes)" (1983) contains some little formulas that produce either...
Forum: Prime Gap Searches 2019-02-15, 20:55
Replies: 23
Views: 2,786
Posted By danaj
Yes, quite a bit faster, albeit I don't know...

Yes, quite a bit faster, albeit I don't know anything as simple as modern primality testing. It still has a terrible growth rate so gets quite slow if you're spoiled by how fast we can do primality...
Showing results 1 to 25 of 906

 
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