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16 (another Prime Pages' Curiosity) |
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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]
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