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+ 34 = pi(144). Note that 34 and 144 are Fibonacci numbers. No larger example of this type is known. [Honaker]

+ The first 34 odd numbers (concatenated) is prime. [Das]

+ 34 is the smallest number which can be expressed as the sum of two primes in four ways. [Murthy]

+ The smallest composite Fibonacci number whose sum of prime factors is a prime. [Gupta]

+ 134 + 233 + 332 + ... + 323 + 332 + 341 is prime. [Patterson]

+ 34 = 3 + 5 + 7 + 19 is the smallest number which is sum of distinct primes whose digits are odd. Note that all the odd digits are used, without repetition. [Capelle]

+ The smallest Fibonacci number f such that neither 6f - 1 nor 6f + 1 are prime. [Necula]

+ pi(34)= !3 + !4, where !3 and !4 denotes subfactorial 3 and subfactorial 4 respectively. [Gupta]

+ 34 = pi(3!*4!). [Firoozbakht]

+ 34!/34# + 1 are twin primes. [Wesolowski]

+ pi(34) = 3!! + 4!!. [Gupta]

+ There are 34 five-digit primes formed from the five odd digits. This means there's a Fibonacci number of Fibonacci-digit primes formed from the Fibonacci number of odd digits. [Silva and Honaker]

+ First occurrence of a run of exactly 34 consecutive integers with an odd number of prime factors has never been found.

(There are 8 curios for this number that have not yet been approved by an editor.)




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