The Distribution of Prime Numbers

In this paper, we discovered a new sequence of all prime numbers which end with a 1 or 9, the sequence defined by 𝑎(𝑛) = (𝑛^2 − 𝑛 − 1)/gcd (𝑏(𝑛), 𝑛^2 − 𝑛 − 1), with 𝑏(𝑛) satisfying the recurcive formula 𝑏(𝑛)=(𝑛 − 1). 𝑏(𝑛 − 1) − 𝑛. 𝑏(𝑛 − 2) and 𝑏(1) = 𝑏(2) = −1, the sequence 𝑎(𝑛) takes only 1’s and primes.

Related Organizations

Sidi Mohamed Ben Abdellah University
Morocco

Keywords

Prime Numbers

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