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The (double) Primorial sieve  &  Prime spirals E-mail

The paper holds a study into verifying large prime numbers with a right-to-left  base 10^m  positional numeral system, without using the operators multiplying and division, see  Base 10^ m numeral system.pdf.
Large integers, like recent Mersenne primes, are broken into pieces based on a  base 10^m  numeral system.
The principles of the Sieve of Eratosthenes are used to close in on the integer to be checked, often making huge leaps.

Describing the proces is simplified by using  32-bit integers  and  base 10^2  or  10^8 numeral systems,  while modern computers nowadays use  64-bit integers  and can accommodate a  10^18 numeral system.
Note that in the  base 10^m  positional numeral system,  m  should be  even  to easier approximate the square root of a very large integer.

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.
Other finds in that project are the  Ulam spiral unraveled.pdf,  the  last digit gap between prime numbers.pdf
and the  segmented prime spirals.pdf,  etc.


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Number systems: Base 10^m  numeral system.