Authors: Marius Coman
In this paper I make the following four conjectures on the Smarandache prime-partial-digital sequence defined as the sequence of prime numbers which admit a deconcatenation into a set of primes: (I) there exist an infinity of primes p obtained concatenating two primes m and n, both of the form 6*k + 1, such that n = m*h – h + 1 , where h positive integer; (II) there exist an infinity of primes p obtained concatenating two primes m and n, both of the form 6*k - 1, such that n = m*h + h - 1 , where h positive integer; (III) there exist an infinity of primes p obtained concatenating two primes m and n, both of the form 6*k + 1, such that n + m - 1 is prime or power of prime; (IV) there exist an infinity of primes p obtained concatenating two primes m and n, both of the form 6*k - 1, such that n - m + 1 is prime or power of prime. Note that almost all from the first 65 primes obtained concatenating two primes of the form 6k + 1 (exceptions: 3779, 4373, 6173, 6719, 6779), and all the first 65 primes obtained concatenating two primes of the form 6k - 1, belong to one of the four sequences considered by the conjectures above.
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[v1] 2016-03-20 03:45:41
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