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Talk:Untouchable numbers: Difference between revisions

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Talk:Untouchable numbers (view source)

Revision as of 05:53, 6 September 2021

484 bytes removed ,  2 years ago
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→‎reduction in the number of (counting) ranges: Thanks
(→‎reduction in the number of (counting) ranges: no idea were to get the right factor for checking)
 
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Limit //100*1000*1000;//10*1000*1000;//5*1000*1000;//1000*1000;
factor //384( to small ) ;//152;//104;//64; // search area = factor*Limit</pre>
:How about using Goldbach conjectue ( tested true > 1e18 ).All numbers are a sum of max three primes<BR>
proper div sum(p*q) = 1+p+q / p<>q and both prime and p*+q < Limit
proper div sum(p*q*r) = 1+p+q+r+p*q+p*r+q*r/ p<>q<>r and all prime and proper div sum(p*q*r) <=Limit
: is limit for checks == limit^(1/3) or limit/3
:<b>EDIT found earlier failure at 300,000</b> used special glasses ;-)
: I'll test it with 1e8 and factor 464 will take ~30min
<pre>
::Still false at 80000000, but correct for 1e8 ?
//url=https://math.dartmouth.edu/~carlp/uupaper3.pdf
<pre>LIMIT = 100000000
100000 1229 1000713863
200000 28572
factor beyond LIMIT 464
300000 43515
runtime for n<= LIMIT 7.972 s
but I get, testing fo 100,000,000 with limit 46,400,000,000 that is 154,666 x 300,000:
Check the rest 46,300,000,000
154,666 is bigger than 0.5 * 300,000
runtime 1193.714 s
100,000 10 13,863 2
200,000 100 528,572
300,000 1000 43,514 < less by 89one
</pre>
10000 1212
:::Maybe Nigel can test up300,000 if the totable 6in millionuupaper3.pdf oneis nighttrue? --[[User:HorsthHorst.h|HorsthHorst.h]] ([[User talk:HorsthHorst.h|talk]]) 0912:5529, 4 September 2021 (UTC)▼
100000 13863▼
:: The uupaper includes the final value, that is 300000 is an untouchable number--[[User:Nigel Galloway|Nigel Galloway]] ([[User talk:Nigel Galloway|talk]]) 15:35, 5 September 2021 (UTC)
1000000 150232▼
::::Thank you.I changed output to include limit.After other modifications the numbers fit to uupaper.<BR>
10000000 1574973
20000000 3184111
30000000 4804331
40000000 6430223
50000000 8060162
60000000 9694467
70000000 11330312
80000000 12967238
90000000 14606549
100000000 16246940
 
real 19m53,838s</pre>
:::I've changed output, to compare with Carl Pommerance values.<BR>
:::Still one off at 6,000,000 936,243 instead of 936,244<BR>
:::Although tested to 46,400,000,000 = 7,733 x 6,000,000<Br>
:::The difference is only one and values after that are right until 80,000,000 ????
<pre>LIMIT = 100,000,000
2262 20011 // check with primes factor
factor beyond LIMIT 465
runtime for n<= LIMIT 13.879 s
Check the rest 46,400,000,000
200,000,000 dT 2.686 s
...
46,300,000,000 dT 2.718 s
46,400,000,000 dT 2.724 s
46,500,000,000 dT 2.727 s
runtime 1249.478 s
1,000 89
10,000 1,212
100,000 13,863
...
1,000,000 150,232
2,000,000 305,290
3,000,000 462,110
4,000,000 619,638
5,000,000 777,672
6,000,000 936,243
7,000,000 1,095,710
8,000,000 1,255,015
9,000,000 1,414,783
10,000,000 1,574,973
20,000,000 3,184,111
30,000,000 4,804,331
40,000,000 6,430,223
50,000,000 8,060,162
60,000,000 9,694,467
70,000,00011,330,312
80,000,00012,967,238
90,000,00014,606,549
100,000,00016,246,940</pre>
▲:::Maybe Nigel can test up to 6 million one night --[[User:Horsth|Horsth]] ([[User talk:Horsth|talk]]) 09:55, 4 September 2021 (UTC)
 
== Number of untouchable numbers up to 1 million ==
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:OK, i tried sieve factors of 62 and 63. The former was one off and the latter spot on so I'm going with that. The time was exactly the same as the factor 64 version because of another change I made to use less memory. I would, of course, have preferred to use a method which didn't involve any guessing such as Nigel's but the timing difference is just too great - the current Go program with a limit of 100,000 and a sieve factor of 14 takes only 6.2 seconds to run and is very easy to understand. --[[User:PureFox|PureFox]] ([[User talk:PureFox|talk]]) 16:36, 14 February 2021 (UTC)
 
== Number of untouchable numbers up to <s>2</s> <s>3</s> 6 million ==
I've calculated 2 million as 305290. As Adrian Monk puts it "I could be wrong, but I never am."--[[User:Nigel Galloway|Nigel Galloway]] ([[User talk:Nigel Galloway|talk]]) 13:11, 17 February 2021 (UTC)
 
Line 133 ⟶ 83:
::it is but how to estimated a good Multiple of LIMIT to find all.
--[[User:Horsth|Horsth]] ([[User talk:Horsth|talk]]) 14:06, 2 September 2021 (UTC)
 
Running F# to 6 million seems to agree with uupaper3.pdf
<pre>
F:\>.\UntouchableP.exe
▲ 100000 -> 13863
200000 -> 28572
30000 -> 43515
400000 -> 58459
500000 -> 73565
600000 -> 88828
700000 -> 104062
800000 -> 119302
900000 -> 134758
▲ 1000000 -> 150232
2000000 -> 305290
3000000 -> 462110
4000000 -> 619638
5000000 -> 777672
6000000 -> 936244
</pre>--[[User:Nigel Galloway|Nigel Galloway]] ([[User talk:Nigel Galloway|talk]]) 15:31, 5 September 2021 (UTC)
 
==Nice recursive solution==
Anonymous user
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