Short remark on Fibonacci-Wieferich primes (original) (raw)

Article

Keywords:
Fibonacci-Wieferich primes; heuristics on distributions of primes with arithmetic constraints; Fibonacci numbers; Wall-Sun-Sun prime; modular periodicity; periodic sequence

Summary:

This paper has been inspired by the endeavour of a large number of mathematicians to discover a Fibonacci-Wieferich prime. An exhaustive computer search has not been successful up to the present even though there exists a conjecture that there are infinitely many such primes. This conjecture is based on the assumption that the probability that a prime ppp is Fibonacci-Wieferich is equal to 1/p1/p1/p. According to our computational results and some theoretical consideratons, another form of probability can be assumed. This observation leads us to interesting consequences.

References:

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