Is 5 the only odd untouchable number?
Is 5 the only odd untouchable number?
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An untouchable number is a number that is not the sum of the proper divisors (the factors of a number except for itself) of any number.
5 is untouchable because 1 is a proper divisor of any number, and the only way to write 5 as a sum of positive integers including 1 is 1 + 4. But any number with 4 as a factor also has two as a factor, so its proper divisors will add to at least 7.
5 is the only odd number known to be untouchable, while there are infinitely many untouchable numbers in total.
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Related questions
What is this?
What is Manifold?
Manifold is the world's largest social prediction market.
Get accurate real-time odds on politics, tech, sports, and more.
Or create your own play-money betting market on any question you care about.
Are our predictions accurate?
Yes! Manifold is very well calibrated, with forecasts on average within 4 percentage points of the true probability. Our probabilities are created by users buying and selling shares of a market.
In the 2022 US midterm elections, we outperformed all other prediction market platforms and were in line with FiveThirtyEight’s performance. Many people who don't like betting still use Manifold to get reliable news.
Why use play money?
Why use play money?Mana (Ṁ) is the play-money currency used to bet on Manifold. It cannot be converted to cash. All users start with Ṁ1,000 for free.
Play money means it's much easier for anyone anywhere in the world to get started and try out forecasting without any risk. It also means there's more freedom to create and bet on any type of question.