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Old 2021-10-23, 11:29   #1
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
Oregon, USA

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Default 2-tuples

Hi all,

I made some changes to my 2-tuples webpage. It was hosted for free by Google.
Here is the Google Sites 2tuple page
I am just putting it here for now.
Can anyone change this to .pdf format and still include the clickable links?
I can't do that with Open Office.

Regards,
Matt
Attached Files
File Type: doc 2 tuples.doc (23.0 KB, 50 views)

Last fiddled with by MattcAnderson on 2021-10-23 at 11:30 Reason: added Google Sites page
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Old 2021-10-23, 13:04   #2
Dr Sardonicus
 
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Quote:
Originally Posted by MattcAnderson View Post
Can anyone change this to .pdf format and still include the clickable links?
I can't do that with Open Office.
This should fill the bill.
Attached Files
File Type: pdf 2 tuples.pdf (125.0 KB, 58 views)
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Old 2021-10-23, 17:09   #3
MattcAnderson
 
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"Matthew Anderson"
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Thanks Dr Sardonicus,
That is exactly what I wanted.
Regards,
Matt
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Old 2022-02-14, 04:27   #4
MattcAnderson
 
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behold,
it might be interesting.

Matt

look

look - pairs 6 apart

look - pairs 8 apart

We can call these octal prime numbers.

Regards,
Matt A

Some of this interesting data is redundant.
More is already stored in the Online Encyclopedia of Integer Sequences (OEIS.org)
See attached for links to existing data.

Regards,
Matt

now 46

OEIS has not incorporated this yet.
Maybe not of general interest.

Matt

now 48

now 50

a good place to stop, for now.

Matt
Attached Files
File Type: pdf a 2 tuple with counting numbers.pdf (402.2 KB, 19 views)
File Type: pdf 2tuple 4 apart.pdf (268.6 KB, 19 views)
File Type: pdf 2tuple 6 apart.pdf (395.8 KB, 22 views)
File Type: pdf 2tuple 8 apart.pdf (256.9 KB, 18 views)
File Type: pdf 2 tuples in OEIS as of January 2022.pdf (129.3 KB, 19 views)
File Type: pdf 2tuple 46 apart with comment.pdf (224.2 KB, 22 views)
File Type: pdf 2tuple 48 apart with comment.pdf (461.9 KB, 23 views)
File Type: pdf 2tuple 50 apart with comment.pdf (355.2 KB, 20 views)
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Old 2022-02-14, 05:05   #5
Batalov
 
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Quote:
Originally Posted by MattcAnderson View Post
a good place to stop, for now.
a good place to stop, for sure.

Look, you just wasted 2.49 Mb of disk space that Mike is paying for - in mere 18 minutes. (Footnote: in Matt's inimitable fashion - the post above was not one post. No. It was eight messages one after another, inside 18 minutes between 1st and 8th. it is a bad thing when you talk to a person and he doesn't wait for your answer and doesn't let you insert a word. No, he keeps bursting into word chunks. Technical name for that is logorrhea - hence the name of this subforum, sounds familiar?)

The real content in those 2.49 Mb is at most of 10Kb of text.
At this rate, you can fill up universe with white noise in several days.

Think about it. ok?

P.S. Consider this an intervention. Which is long overdue. Were you actually idle around those 18 minutes? No - see that other thread: it is exactly like this one. Excited? No, sorry, -- instead we are very worried.
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Old 2022-02-14, 05:28   #6
MattcAnderson
 
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"Matthew Anderson"
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I gave Mike $100 and on another occasion, $20.
I did it on the down low, but now I feel I have to defend myself.

So I contribute. I help keep mersenneforum.org going - monetarily


And, this is a personal blog.

Cheers

P.S. This is my hobby. We are not that much different.

Last fiddled with by MattcAnderson on 2022-02-14 at 05:31
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Old 2022-02-14, 08:49   #7
MattcAnderson
 
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Default All prime numbers are equal in value.

I'm a bit stirred up from the previous post.

How is the largest prime number known to human kind
more important that a data set of k-tuples?

I say they are the same.
Both are of marginal importance.

Are there any real world problems that can be solved
by knowing a bigger prime number?

I say no. At least not today, and not in the short term future.

We do these calculations because we can. The challenge is worth it.

So, I paid for my blog, and I will put whatever I want on it.

Good day sir.

Regards,
Matt Anderson
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Old 2022-02-14, 08:57   #8
paulunderwood
 
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Maybe you should just put the Maple code and results in "code tags" not bloated PDFs, after all is anyone seriously going to a) open them via a download? and b) print them out?

(Good on you for your monetary contributions to the forum -- why spoil it with bloat?)
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Old 2022-02-14, 21:01   #9
MattcAnderson
 
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Default 2 tuple with difference of 46

Hi all,

I choose a difference between prime numbers
of 46 because that is the smallest even number
that is not in the database at OEIS.org

In my humble opinion, this data is as exciting as
M48 or M51.

From mersenne.org/primes/ we see that
2^(82,589,933) - 1 is a prime number.

But we really want the 100 smallest 2-tuples
that are 46 apart <wink>.

I show my Maple code, and my list of prime pairs.


Code:
# This is Maple code with some screen output.

> m := Matrix(3, 100);
> print(`output redirected...`); 
                           
> for a to 100 do 
	m[1, a] := a; 
	end do;
> m[1, 7];
                                      7
> # so column 1 of m Matrix contains 1,2,3, ... ,100.

> count := 1;
                                      1
> for a to 1000 do 
if isprime(a) and isprime(a+46) 
then    m[2, count] := a;
	m[3, count] := a+46; 
	print("interesting data", a, "  ", a+46); 
	count := count+1; 
end if; 
end do;

# now column 2 of m Matrix contains the smaller of pairs with difference 46.
# print to screen

List of primes p such that p+46 is also a prime number.
Code:
                       "interesting data", 7, "  ", 53
                      "interesting data", 13, "  ", 59
                      "interesting data", 37, "  ", 83
                      "interesting data", 43, "  ", 89
                      "interesting data", 61, "  ", 107
                      "interesting data", 67, "  ", 113
                     "interesting data", 103, "  ", 149
                     "interesting data", 127, "  ", 173
                     "interesting data", 151, "  ", 197
                     "interesting data", 181, "  ", 227
                     "interesting data", 193, "  ", 239
                     "interesting data", 211, "  ", 257
                     "interesting data", 223, "  ", 269
                     "interesting data", 271, "  ", 317
                     "interesting data", 307, "  ", 353
                     "interesting data", 313, "  ", 359
                     "interesting data", 337, "  ", 383
                     "interesting data", 373, "  ", 419
                     "interesting data", 397, "  ", 443
                     "interesting data", 421, "  ", 467
                     "interesting data", 433, "  ", 479
                     "interesting data", 457, "  ", 503
                     "interesting data", 463, "  ", 509
                     "interesting data", 523, "  ", 569
                     "interesting data", 541, "  ", 587
                     "interesting data", 547, "  ", 593
                     "interesting data", 571, "  ", 617
                     "interesting data", 601, "  ", 647
                     "interesting data", 607, "  ", 653
                     "interesting data", 613, "  ", 659
                     "interesting data", 631, "  ", 677
                     "interesting data", 673, "  ", 719
                     "interesting data", 727, "  ", 773
                     "interesting data", 751, "  ", 797
                     "interesting data", 811, "  ", 857
                     "interesting data", 883, "  ", 929
                     "interesting data", 907, "  ", 953
                     "interesting data", 937, "  ", 983
                     "interesting data", 967, "  ", 1013
I hope you enjoyed this content everybody.
Cheers.
Now your life is complete since you know that 967 and 1013 are prime pairs. <grin>
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Old 2022-02-14, 21:34   #10
Uncwilly
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Mod note: 3 different low post 2-tuple threads merged.
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Old 2022-02-15, 15:45   #11
Dr Sardonicus
 
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Quote:
Originally Posted by Dr Sardonicus View Post
<snip>
Some possibly interesting questions about pairs of primes differing by 46: They need not be consecutive primes. In fact, consecutive primes differing by 46 are fairly thin on the ground, at least initially, compared to all pairs of primes differing by 46. so, one may ask: How many "admissible k-tuples" are there whose first and last terms differ by 46? How large can k be? And what is the relative contribution of each to the pairs of primes differing by 46?
By looking at the Patterns of prime k-tuplets & the Hardy-Littlewood constants page of Cybertronic's excellent pzktupel site, I was able to cull admissible k-tuples for k = 8 to 12. At this point, it looks to me like 12 is as large as k can be.

(12) 0 4 6 10 16 18 24 28 30 34 40 46 48 (13-tuplet)

(11) 0 6 10 16 18 22 28 30 36 42 46 48 52 58 60 66 70 72 76 (19-tuplet)

(10) 0 4 10 16 18 24 28 36 40 46 54 58 60 66 70 78 84 88 94 100 106 108 114 120 124 126 130 136 138 144 148 150 154 156 (34-tuplet)

(9) 0 4 6 16 28 30 34 36 46 48 58 60 64 66 70 84 88 90 94 100 106 108 114 118 126 130 136 144 148 150 156 160 168 174 178 184 190 196 198 204 210 214 220 226 228 234 238 240 244 246 (50-tuplet)

(8) 0 4 6 16 30 34 36 46 48 58 60 64 70 78 84 88 90 94 100 106 108 114 118 126 130 136 144 148 150 156 160 168 174 178 184 190 196 198 204 210 214 216 220 226 228 234 238 240 244 246 (50-tuplet)

EDIT: This topic affords an illustration of how misleading the behavior of small numbers can be. First, I look for pairs of primes less than 500000 which differ by 48. I classify them by whether their indices differ by 1, 2, ..., 13. Out of the 9298 pairs found, only 67 of them are consecutive. [OK, I used pseudoprime() instead of isprime(). And I cheated on the size of the vector w. I guessed too big in a dry run, and then pared it down.]

Code:
? m=precprime(500000-48);n=primepi(m);v=primes(n);w=vector(13);for(i=1,n,p=v[i];q=p+48;if(ispseudoprime(q),k=primepi(q)-primepi(p);w[k]++;));for(i=1,13,print(i" "w[i]));print(sum(i=1,13,w[i]))for(i=1,13,print(i" "w[i]));print(sum(i=1,13,w[i]))
1 67
2 565
3 1636
4 2418
5 2360
6 1446
7 558
8 183
9 46
10 10
11 6
12 2
13 1
9298
?
But as you look at larger numbers, pairs of consecutive primes differing by 48 become more common (or less uncommon) than pairs of primes differing by 48 with indices differing by more than 1. I look for the first occurrence of each possibility, a bit further out. I know, nextprime() only promises a number that a BPSW test does not prove composite. If you want to run isprime() or something to check that the outputs are actually prime, go for it.

Code:
? ok=0;m=nextprime(10^10);p=m;until(ok,m=nextprime(p+1);if(m-p==48,ok=1;print(m),p=m));m=nextprime(10^10);p=m;ok=0;until(ok,m=nextprime(p+1);if(m-p<48&&ispseudoprime(m+48),ok=1;print(p" "m-p" "48),p=m))
10000000391
10000000319 24 48
? ok=0;m=nextprime(10^20);p=m;until(ok,m=nextprime(p+1);if(m-p==48,ok=1;print(m),p=m));m=nextprime(10^20);p=m;ok=0;until(ok,m=nextprime(p+1);if(m-p<48&&ispseudoprime(m+48),ok=1;print(p" "m-p" "48),p=m))
100000000000000000349
100000000000000000391 2 48
? ok=0;m=nextprime(10^50);p=m;until(ok,m=nextprime(p+1);if(m-p==48,ok=1;print(m),p=m));m=nextprime(10^50);p=m;ok=0;until(ok,m=nextprime(p+1);if(m-p<48&&ispseudoprime(m+48),ok=1;print(p" "m-p" "48),p=m))
100000000000000000000000000000000000000000000001611
100000000000000000000000000000000000000000000001527 36 48
? ok=0;m=nextprime(10^75);p=m;until(ok,m=nextprime(p+1);if(m-p==48,ok=1;print(m),p=m));m=nextprime(10^75);p=m;ok=0;until(ok,m=nextprime(p+1);if(m-p<48&&ispseudoprime(m+48),ok=1;print(p" "m-p" "48),p=m))
1000000000000000000000000000000000000000000000000000000000000000000000005221
1000000000000000000000000000000000000000000000000000000000000000000000039987 42 48
? ok=0;m=nextprime(10^100);p=m;until(ok,m=nextprime(p+1);if(m-p==48,ok=1;print(m),p=m));m=nextprime(10^100);p=m;ok=0;until(ok,m=nextprime(p+1);if(m-p<48&&ispseudoprime(m+48),ok=1;print(p" "m-p" "48),p=m))
10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000044589
10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000109677 22 48
? ok=0;m=nextprime(10^120);p=m;until(ok,m=nextprime(p+1);if(m-p==48,ok=1;print(m),p=m));m=nextprime(10^120);p=m;ok=0;until(ok,m=nextprime(p+1);if(m-p<48&&ispseudoprime(m+48),ok=1;print(p" "m-p" "48),p=m))
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001071
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000039873 46 48
? ok=0;m=nextprime(10^200);p=m;until(ok,m=nextprime(p+1);if(m-p==48,ok=1;print(m),p=m));m=nextprime(10^200);p=m;ok=0;until(ok,m=nextprime(p+1);if(m-p<48&&ispseudoprime(m+48),ok=1;print(p" "m-p" "48),p=m))
100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000187209
100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001315933 8 48

Last fiddled with by Dr Sardonicus on 2022-02-15 at 23:31 Reason: As indicated
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