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November 14
Curious numbers

I saw a tweet on my @SofARMaths account yesterday from Nalini Joshi @monsoon0 which read "I love all numbers great & small. Why are there so many anthropomorphic adjectives for them: odious, evil, perfect, nice, pernicious?" This prompted a frivolous exchange of tweets during which I asked whether there are any "curious" numbers.

I decided to call a curious number one that belongs to the set {Cn} where Cn is the product of the first n prime numbers +1. This is a definition that has been buzzing around my head for many months, probably years, since I first encountered Euclid's proof that the number of primes is infinite.

When I asked myself whether 200560490131 is prime I came across a link to primorial numbers which shows that this area is already well researched. Oh well – perhaps we can classify these and other numbers by the number of prime factors they have. Is there a name for numbers which are the product of exactly 2 prime numbers such as 30031?


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