Number Theory

    

Conjecture on an Infinity of Subsequences of Primes in Smarandache Prime Partial Digital Sequence

Authors: Marius Coman

In this paper I make the following conjecture on an infinity of subsequences of primes in Smarandache prime-partial-digital sequence, defined as the sequence of prime numbers which admit a deconcatenation into a set of primes: for any prime p which admits a deconcatenation in k primes larger than 3 is true that there exist a number of k sequences of primes P1, P2,...,Pk, each one having an infinity of prime terms which also admit a deconcatenation in prime numbers, obtained replacing a prime q in p with primes having the same digital root as q (example: for the prime 547 there exist an infinite sequence of primes obtained replacing 5 with primes having the digital root equal to 5 (2347, 13147, 14947, ...) and also an infinite sequence of primes obtained replacing 47 with primes having the digital root equal to 2 (5101, 5227, 5281,...).

Comments: 2 Pages.

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Submission history

[v1] 2016-03-26 23:53:47

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