Charles Ashbacher
F. Smarandache has defined many sequences of integers formed by concatenating the positive integers in specific ways. A question that is often asked about most of these sequences concerns the number of primes in the sequence. As Paul Erdos pointed out, determining how many primes are in sequences of this type is a problem that the current state of mathematical knowledge is unprepared to solve. In general, the sequences grow rather fast, so after a very short time, the terms are too large for modern computers to determine if they are prime. The only hope is to find some property of the elements of the sequence that can be used to very quickly determine if it can be factored.
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