Number Theory


Observations on Poulet Numbers Having Only Odd Digits Based on Their Reversals

Authors: Marius Coman

The set of Poulet numbers having only odd digits is: 1333333, 1993537, 3911197, 5351537, 5977153, 7759937, 11777599...(22 from the first 7196 Poulet numbers belong to this set). Question: is this sequence infinite? Observations: the numbers n*P + R(P) – n respectively P + n*R(P) - n, where R(P) is the reversal of P and n positive integer, are often primes. Examples: for P = 1333333, the number 1333333 + 3333331 – 1 = 4666663, prime; also 3*1333333 + 3333331 – 3 = 7333327, prime; also 5*1333333 + 3333331 – 5 = 9999991, prime. For the same P, the number 1333333 + 2*3333331 - 2 = 7999993, prime; also the number 1333333 + 4*3333331 - 4 = 14666653, prime.

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[v1] 2018-02-12 14:37:55

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