Illustrious Problems

Looking at a list of smaller twin numbers, we noticed that prime number 5 appears to be the only prime number that appears in two twin prime pairs (3, 5) and (5, 7). Is this the only prime number that is a member of two twin pairs, or in other words, is the triplet (3, 5, 7) the only twin prime number triplet  

As far as we are aware, this question has not been previously posed. There is a question relating to Fibonacci numbers that bears some similarity. The Fibonacci numbers [20] we will meet later when discussing the count of Kekuld valence structures for a special class of benzenoid hydrocarbons. The initial Fibonacci numbers are 

They satisfy the simple recursion + F 2 with seed values F = and F2 

Fibonacci numbers illustrated on the count of growth of annual branches of 

Here is a mathematical question raised and still not answered Is 144, the 12th member in the sequence, the only Fibonacci number that is a square of a number, 144 being 12 As far as we know, this is an unsolved problem. We have not included this problem in our list of problems as we could not trace its origin. 

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In view that the main tool to be used here is mathematics, it seems appropriate as an introduction to review a selection of solved and unsolved problems in mathematics. We do not assume familiarity of readers with details of mathematics, discrete or not, and what we need we will clearly explain. We will start with a few problems that have been considered in antiquity, followed with a few so-called famous problems, the problems that can be easily understood even by laymen, but the solving of which may cause even outstanding professionals to have difficulties. In addition, we have selected a few illustrious problems. According to Webster s Dictionary of Synonyms Antonyms [8], illustrious stands for something enduring and merited honor and glory. We feel that the selected problems deserve such a title. 

It may have been accidental that Hilbert had 23 problems, just the same as the number of definitions with which Euclid started his first book Be this as it may, we decided, to adorn our book with 23 problems—this is not to imply any pretense about the importance of our problems, but a sign of respect for such illustrious persons such as Euclid and Hilbert. 

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