Generalized Andrica Conjecture

8/14/2019 Generalized Andrica Conjecture

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Numerical plots for the first primes show that the solutions of

tend to be confined in the interval and according to generalized Andrica conjecture

one hopes that this behavior remains true as .

The following plots of were created with Wolfram's Mathematica 5.2, the function

plot range was cut off at , so the edge of the plateau is visualizing the exact

solutions of the equation .



Plots for the first 200 primes. This plot most clearly visualizes the putative minimal solution

known also as the Smarandache constant, which seems to occur for .



Plots for the first 1000 primes.



Plots for the first primes.
















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See Also: Florentin Smarandache, Smarandache function

Cross-references: plateau, edge, cut, range, Mathematica, interval, inequality, Smarandache constant, Florentin

Smarandache, twin primes, difference, minimal, solutions, equation, positive, negative, clear, open problem,Andrica conjecture, prime number, function

There are 2 references to this entry.

This is version 29 of generalized Andrica conjecture, born on 2007-06-21, modified 2007-07-16.

Object id is 9636, canonical name is GeneralizedAndricaConjecture.

Accessed 1336 times total.

Classification:



AMS MSC: 11A41 (Number theory :: Elementary number theory :: Primes)

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Generalized Andrica Conjecture