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Maps represent powerful tools to show the spatial variation of a variable in a straightforward manner. A crucial aspect in map rendering for its interpretation by users is the gamut of colours used for displaying data. One part of this problem is linked to the proportion of the human population that is colour blind and, therefore, highly sensitive to colour palette selection. The aim of this paper is to present a function in R - \texttt{cblind.plot} - which enables colour blind people to just enter an image in a coding workflow, simply set their colour blind deficiency type, and immediately get as output a colour blind friendly plot. We will first describe in detail colour blind problems, and then show a step by step example of the function being proposed. While examples exist to provide colour blind people with proper colour palettes, in such cases (i) the workflow include a separate import of the image and the application of a set of colour ramp palettes and (ii) albeit being well documented, there are many steps to be done before plotting an image with a colur blind friendly ramp palette. The function described in this paper (\ttt{cblind.plot}), on the contrary, allows to (i) automatically call the image inside the function without any initial import step and (ii) explicitly refer to the colour blind deficiency type being experienced, to further automatically apply the proper colour ramp palette.

This paper attempts to answer the riddle of why Ω(m), the sum of the exponents of the prime decomposition of m = (2x-2)(2x-3)(2x-5) …(2x-qb) [where qb is the bth prime and b = π(x), the number of primes not exceeding x], always appears to lie in the region of 2π(x), where π(x) is the number of primes not exceeding x. It turns out that an application of the Hardy Ramanujan Theorem shows Ω(m) is almost always exceeded by 2π(x), which has the logical implication the Goldbach’s Conjecture is “almost always true”.

This translation has been withdrawn due to certain imperfections and mistakes, which are corrected in the version uploaded at The Euler Archive (see E65 at http://www.eulerarchive.org/), This paper has been withdrawn by the author