Talk:Rare numbers: Difference between revisions
→21 digit rare numbers: found some 22s
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::::To reliably go any further than this would require the use of big integers (unpleasant and relatively slow in Go) as signed 64 bit integers have a 19 digit maximum. It might be possible to use unsigned 64 bit integers (20 digit maximum) though this would require some fancy footwork to deal with negative numbers and subtraction. So I think that's my lot now :) --[[User:PureFox|PureFox]] ([[User talk:PureFox|talk]]) 20:04, 2 October 2019 (UTC)
== 21+ digit rare numbers ==
Well, one anyway (so far). I tweaked the BigInteger version of the C# program to skip to start at 21 digits. Around 6 hours, I got the first one: '''219,518,549,668,074,815,912''', with the sum = '''20,953,210,268^2''', and the difference = '''8,877,000^2'''. Still have no idea how long it will take to finish the block of 21 digit numbers. Since the difference found so far was a relatively low number, it probably has quite a while to go.
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::I see this BigInteger conversion attempt as a means of reaching a few 21 digit numbers (which it did) and a means to reveal any shortcomings in the existing ulong algorithm which don't translate well to the BigInteger version (which it also did, I guess). If only it wasn't so impractically slow. If I could get it an order of magnitude faster, it would easier to persue this further. Creating a multi-tasking version would probably only go 2 to 4 times faster.--[[User:Enter your username|Enter your username]] ([[User talk:Enter your username|talk]]) 06:57, 24 October 2019 (UTC)
There only seem to be 5 21 digit rare numbers, so I started looking at 22 digits. Here are a few found so far:
90 (2,788,047,868,437,576,408,872)
91 (2,788,047,848,617,776,408,872)
92 (2,788,047,888,617,376,408,872)
93 (2,788,047,668,617,596,408,872)
This is probably only 10 - 15% of the search space. There may be many more to go...
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