User Portlet

Author of the following website dealing with the Ulam spiral: https://www.ulamspiralmethod.com

Contents in brief: The site is purposed to demystify the following 2 aspects of the spiral: 1) The diagonal orientation of the linear groups of contiguous numbers. 2) The discontinuities due to which these linear groups exist as finite and separate entities.

Prime numbers are definable as numbers per 6n±1, as such they are just a subset of ALL the numbers per 6n±1, because ALL the numbers per 6n±1 would contain prime numbers AND composite numbers.

When ALL the numbers per 6n±1, prime- & composite-, are placed on the Ulam spiral, the result shows endless, uninterrupted, diagonally orientated linear rows of numbers. all adjacent parallel pairs of these rows have an identical space between them. (There is also a subset of evenly distributed solitary numbers that are not part of any row.)

Thus, when the Ulam spiral is populated by ONLY the prime numbers per 6n±1 the endless rows of numbers mentioned in the preceding paragraph are now fragmented by the absence of the composite numbers per 6n±1. These fragments still preserve the diagonal orientation of the endless rows of numbers mentioned in the preceding paragraph.

(The Ulam spiral populated by the prime numbers per 6n±1 is somewhat different from the standard Ulam spiral because: a) 2 & 3 are not represented because they are not primes per 6n±1. b) 1 is represented because it is a number per 6n±1 @ n = 0.)

Besides having an extensive Ulam spiral populated by prime numbers per 6n±1 having an equally extensive Ulam spiral populed by composite numbers per 6n±1 next to it would be a great analytical aide.

Since all these numbers per 6n±1, prime-& composite-, are in fact "pinned in place" by the multiples of 6, (that is: numbers per 6n) It is useful to also contemplate an Ulam spiral populated by only the multiples of 6, for analytical purposes.