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Talk:Untouchable numbers: Difference between revisions
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I've reduced the number of ranges for counting untouchable numbers. It seems the upper limit for searching for touchable numbers was far higher than I guesstimated. -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk:Gerard Schildberger|talk]]) 09:28, 9 February 2021 (UTC)
:I have checked counting ranges, but, as Nigel stated , that's not the way to get an reliable result, when changing the upper limit.
<pre>
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 ;-)
<pre>
//url=https://math.dartmouth.edu/~carlp/uupaper3.pdf
100000 13863
200000 28572
300000 43515
but I get, testing fo 100,000,000 with limit 46,400,000,000 that is 154,666 x 300,000:
154,666 is bigger than 0.5 * 300,000
100,000 13,863
200,000 28,572
300,000 43,514 < less by one
</pre>
:Maybe Nigel can test 300,000 if the table in uupaper3.pdf is true? --[[User:Horst.h|Horst.h]] ([[User talk:Horst.h|talk]]) 12:29, 4 September 2021 (UTC)
:: 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)
::::Thank you.I changed output to include limit.After other modifications the numbers fit to uupaper.<BR>
== 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)
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::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==
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