The smallest prime power of a prime power of a prime (2^2^2). [Woods]
The smallest number which is the sum of two distinct odd primes in two ways, i.e., 16 = 3 + 13 = 5 + 11. [Honaker]
La Symphonie Primordiale (The Prime Numbers Symphony) is a single movement work for orchestra lasting some 16 minutes.
"Take a number n in base b, and append one more digit to get the nth prime." The first base for which this puzzle has no solutions is 16. [Hartley]
16 is the only two-digit number m such that m^2^0+1,
m^2^1+1, & m^2^2+1 are primes. [Kazemi]
16 is the smallest square which is difference of two prime
squares. [Capelle]
The smallest square whose reverse is prime.
[Capelle]
222
is the smallest number n such that 3 + n, (3*5) + n,
(3*5*17) + n, (3*5*17*257) + n, (3*5*17*257*65537) + n are
all primes. Note that 3, 5, 17, 257 and 65537 are the known
Fermat primes, with the property
(F0*F1*F2*...*Fn-1)
+ 2 = Fn [Capelle]
16^(1+6)+(1+6) is prime. [Silva]
sigma(16^16)+16^16 is prime and the length of this prime
has the same property. [Firoozbakht]
2^4 = 3*5 + 1 is the only solution of n^4 = p*(p+2) + 1 with a twin prime pair (p,p+2), because n^4 = (n^2-1)*(n^2+1)+1 and n^2-1=(n-1)*(n+1) prime <=> n=2. [Krug]
|
