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User:A. Lamek

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My interests

I come from Germany, NRW.

I'm interested in numbers, especially Mersenne Primes and Wieferich Primes. However my level of understanding of number theory is nowhere near that of a mathematicians. Please have little bit of patience with me. Email: blackpuma65@googlemail.com

My favored sequences

  1. Mersenne Primes A000043, A247473
  2. Wieferich Primes A001220, A001576

My assumptions


Mersenne primes: Factors

Mersenne prime numbers , which are not prime, divided by . In this known formula can the values 1, 2, 3, 4, etc.
So that the divider , , , etc could be.
According to my observation, there are, however, gaps in , where no divider occur. These gaps have a mathematically calculable uniformity:


ie.






Mersenne numbers (nonprimes): binomially or triangular !?






































Wieferich primes




A new property of Wieferich primes:














This formula shows that from one base of exponent |E|



2 Wieferich primes (1093, 3511) can be calculated.

My last hunch is that the exponent || is calculated as follows:







Only for there an appropriate solution. If the next Mersenne prime, than gives the next 2 Wieferich primes with





footnote:
[1] by Johnson (1977) (see A note on the two known Wieferich Primes)

  • his formula for the Wieferich primes is
    • " (base 10)"
    • " (base 10)"