With all my summer activities I was quite lazy for the number facts posts. I am quite sorry for those of you that were really into this posts. But in the past weeks I have tried to make time to write these number facts. So here are some interesting ones:

**1. Number 27: **It is the only positive integer that is 3 times the sum of its digits.

Also, 27 is a decagonal number. A *decagonal number* is a figurate number that extends the concept of triangular and square numbers to the decagon (a ten-sided polygon). However, unlike the triangular and square numbers, the patterns involved in the construction of decagonal numbers are not rotationally symmetrical.

**2. Number 7: **For this number I have found quite some interesting types of primes I never new before. So, 7 is the fourth prime number and a Mersenne prime. It is also a Newman–Shanks–Williams prime, a Woodall prime, a factorial prime, a lucky prime, a happy number (happy prime), a safe prime (the only Mersenne safe prime), and the fourth Heegner number. Quite some types… I have left the Wikipedia link to all these things if you want to read more.

Seven is also the lowest natural number that cannot be represented as the sum of the squares of three integers. And more on the complicated mathematics: 7 is the only dimension, besides the familiar 3, in which a vector cross product can be defined ( I think it is extremely interesting).

Hope you enjoyed this small post. Have a wonderful day and a great week. Thank you for your support. Hope you are all having fun this summer. Thank you for your help and support. Thank you for reading. You can find me on Facebook, Tumblr, Google+, Twitter, Instagram and Lettrs, I will try to post there as often as possible. *Don’t forget that maths is everywhere! Enjoy! *

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Some other facts about your numbers:

27. The smallest number such that and each have exactly three prime factors counting their multiplicity.

7. (I really like this one): Of the the two primes (the other being 5) which appears most often as the third prime factor of an integer (1 time in 30)

J-M. De Koninck, “Those Fascinating Numbers”, AMS, 2009.

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