Prime number cross

The prime number cross is shown in figure 1. Because of another property... 

Figure 2.3 Eight-group periodic table of the 81 stable elements, in spiral form available sites on the prime-number cross, starting from zero, number...

In Figure 5.6 we arrange the natural numbers along a spiral with a pitch of 24. All prime numbers, except for 2 and 3, occur on eight radial lines as p = 6n 1. By mapping the natural elements to these radial lines the periodicity of 16 = 2 x 8 is accounted for at the same time as the nuclide periodicity of 24. This arrangement is known as Plichta s prime-number cross. It has the remarkable property that the sum of all numbers over any complete cycle is given by... 

His claim was vindicated with the discovery of atomic number, but the theme remained undeveloped until it was conjectured by Plichta [6] that the electron configuration of atoms is mapped by the distribution of prime numbers. Based on the observation that all prime numbers >3 are of the type 6n 1, he defined a prime-number cross that intersects a display of natural numbers on a set of concentric circles with a period of 24. In Fig. 4, the construct is shown, rearranged as a number spiral. Noting that the numbers on each cycle add up to... 

Since 14 is crossed off the list, box all the numbers that remain on the list. They are all the prime numbers less than or equal to 29 ... 

Fig. 4 The natural numbers arranged on a spiral with a period of 24. All prime numbers >3 and of the form 6n 1 occur on eight straight lines of the cross, which has been interpreted [6] to simulate the electronic structure of atoms...

Figure 10.85 The first four prime knots. The number denotes the number of crossings, while the subscript is the order of the knot. (Reprinted with permission from [98]).

In support of his proposal, Tauber pointed out that For certain knots Ze = 0. This is exactly as it should be, for precisely these knots are identical with their mirror images. Similarly, Walba asserted that The number of 8s and >cs are summed arithmetically. If there are the same number of 8 and X crossings, then the knot must be topologically achiral. Contrary to these assertions, however, alternating knots whose writhe is zero are not necessarily amphicheiral The simplest example is knot 84. Nineteen of the 32 10-crossing prime knots with writhe zero are topologically chi ral, and 13 of these are alternating.144 Two hundred... 

The next number after 2 that is not a multiple of 2 (not crossed off the list) is 3. Consequently, it is prime. Box it and cross off all the multiples of 3. Some of them were crossed off the list earlier ... 

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