Algorithmic number theory
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Many researchers study prime numbers for the curiosities that they possess rather than the position they occupy at the foundations of Number Theory. This study may be in any numbers of areas from applications to multimedia to searching for special or unusual primes. It is truly awe inspiring to see how much time can be expended on prime numbers without a realistic application.In this article, a sequence of prime numbers, called Recursive Prime Numbers, is identified before a complete search is undertaken to verify that the sequence is finite by finding all existing prime numbers of the specified form. This could be done with considerable effort by hand, but here a simple computer program has been used to speed the calculations. So now the question must be answered; what are recursive prime numbers. The easiest way to answer that is to say that a prime number is recursively prime if the number is prime can be constructed by adding a digit to an already recursive prime number.