Number Theory


Primes of the Form N∙P+R(P)-N Where P Primes Having Only Odd Digits and R(P) Their Reversals

Authors: Marius Coman

In a previous paper I noticed that the numbers n*P + R(P) – n respectively P + n*R(P) - n, where P are Poulet numbers having only odd digits, R(P) the reversals of P and n positive integer, are often primes. In this paper I notice that the same is true for primes having only odd digits (see A030096 in OEIS for a list of such primes). Taken thirteen randomly chosen consecutive primes P having nine (odd) digits (from 971111137 to 971111993) I see that for all of them there exist at least a value of n smaller than 15 for which the number n*P + R(P) – n is prime (for 971111591, for instance, there exist four such values of n: 9, 11, 14, 15; for 971111137 three: 2, 4, 7; for 971111551 also three: 1, 2, 6; for 971111959 also three: 1, 9, 10; for 971111993 also three: 5, 6, 14).

Comments: 2 Pages.

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Submission history

[v1] 2018-02-13 02:20:28

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