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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) 34 = (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] 1^{34} + 2^{33} + 3^{32} + ... + 32^{3} + 33^{2} + 34^{1} 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] (34)= !3 + !4, where !3 and !4 denotes subfactorial 3 and subfactorial 4 respectively. [Gupta] 34 = (3!*4!). [Firoozbakht] 34!/34# + 1 are twin primes. [Wesolowski] (34) = 3!! + 4!!. [Gupta] There are 34 fivedigit primes formed from the five odd digits. This means there's a Fibonacci number of Fibonaccidigit primes formed from the Fibonacci number of odd digits. [Silva and Honaker] 7^34+34 is the smaller of only two nontitanic primes of form 7^n+n, (the other is for n=48). [Loungrides] The number of the distinctdigit primes each consisting of all of the odd digits. These are: 13597, 13759, 15739, 15937, 15973, 17359, 17539, 19753, 31957, 37159, 37591, 37951, 39157, 51973, 53197, 53719, 53791, 53917, 57139, 57193, 71359, 71593, 73951, 75193, 75391, 75913, 75931, 79153, 79531, 91573, 91753, 95317, 95713, 95731. [Loungrides] First occurrence of a run of exactly 34 consecutive integers with an odd number of prime factors has never been found. Along with 34+1, the smallest pair of consecutive integers that are both composite and reverse primes. [Gaydos]
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