The (double) Primorial sieve & Prime spirals |
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The primorial sieve is a new algorithm in mathematics to distinguish prime numbers. The primorial sieve can be used to find all prime numbers up to a specific integer value and has advantages over the solid Sieve of Eratosthenes.

The primorial sieve can also be used as a double sieve within a specific range of (very) large integers.

Its basic function mimics Pritchard's Wheel Factorization (1982), but the primorial sieve is more sophisticated.

See the (double) primorial sieve.pdf.

The findings of the (double) primorial sieve offered the opening for solving the Ulam spiral conundrum.

The mystery of the Ulam spiral (1963) is cracked by the discovery of the eight families of functions that capture all natural numbers, see the unraveling of the Ulam spiral.pdf.

The unraveled counterclockwise Ulam spiral with startvalue 0 gave the opening to the infinitely many segmented prime spirals, see segmented prime spirals.pdf.

It is defined that the Ulam spiral is a Ulam four-quarter sprial, and thus a prime spiral with four segments.

Downwards are the prime spirals with respectively three, two and one segments.

Upwards are the prime spirals with five, six, etc segments.

The base 10^{m} numeral system evolved from the (double) primorial sieve, which is one of the results of the hunch to place a prime number on the short leg of a primitive Pythagorean triangle.

The right-to-left base 10^{m} positional numeral system is the result of a study into verifying large prime numbers, without using the operators multiplying and division.

The final product of the Base 10^{m} numeral system.pdf was completed januari 2022.

Since the primorial sieve, the unraveling of the Ulam spiral and the segmented prime spirals are relative new, all suggestions and remarks are welcome.
They can be sent to: **info@primorial-sieve.com**

Ing. J.I.M. (Hans) Dicker MEd.

The Netherlands

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