# 17

This number is a prime.

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Prime Numbers CD Image J. Neptune © 1994 |

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 F_{n} = 2^{2n} + 1 (with n = 2), and hence not a Higgs prime for powers below 2^{n}. [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 4*p*# + 1
is the square of a prime. [Beedassy]

The smallest prime whose binary expansion (10001_{2}) 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]