What are all the prime number for 16 to 32?

1 Answer
George C.
Nov 5, 2016

#17, 19, 23, 29, 31#

Explanation:

The prime numbers between #16# and #32# are:

#17, 19, 23, 29, 31#

The odd composite numbers in that range are:

#21 = 3xx7#

#25 = 5xx5#

#27 = 3xx3xx3#

#color(white)()#
Bonus

Of the prime numbers we list, two are special:

#17 = 2^(2^2)+1#

which is one of the few known Fermat primes.

Pierre de Fermat conjectured that any number of the form #2^(2^n)+1# is prime, but it fails for all known values of #n# greater than #4#

#17# has many other interesting properties, e.g. It is the number of different possible symmetries of wallpaper patterns. It is also the only prime number equal to the sum of the digits of its cube: #17^3 = 4913# and #4+9+1+3 = 17#.

#color(white)()#

#31 = 2^5-1#

which is a Mersenne prime, being of the form #2^p-1#

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