17
This number is a prime.
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| Prime Numbers CD Image J. Neptune © 1994 |
The smallest prime that is both the sum of a prime number of consecutive composites, and also, the sum of a composite number of consecutive primes: 17 = 8 + 9 = 2 + 3 + 5 + 7. [Beedassy]
The only number n having n partitions into prime parts. [Beedassy]
The smallest prime (emirp) equidistant both between two
Mersenne primes (3 and 31) and between two perfect numbers
(6 and 28). [Beedassy]
All whole distances up to 17 can be measured using a Golomb
ruler bearing as few as six marks. [Beedassy]
In France, one dials 17 to call for Police Help in
emergency. [Beedassy]
The first prime that is not a Higgs prime for squares or cubes. This follows from the fact that 17 is a Fermat prime Fn = 22n + 1 (with n = 2), and hence not a Higgs prime for powers below 2n. [Beedassy]
In Mauritian Creole rhetoric, the number 17 is used as a figure of speech to denote a pretty young lady. [Beedassy]
The largest known prime p such that 4p# + 1
is the square of a prime. [Beedassy]
The smallest prime whose binary expansion (100012) contains a greater (prime) number of 0's than that of 1's. [Beedassy]
The smallest emirp p such that the digits of all
primes up to p add up to an emirp: 2 + 3 + 5 + 7 + 1
+ 1 + 1 + 3 + 1 + 7 = 31. [Beedassy]
The smallest emirp that remains an emirp when each digit is
replaced by its square: 149. [Beedassy]
The emirp number of letters in the classic metaphore
"The atoms of numbers" in reference to the primes.
Note that concatenating each word's number of letters forms
an emirp with each distinct prime digit: 3527. [Beedassy]