The (double) Primorial sieve & Prime spirals |
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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.

Number systems: Base 10*^m* numeral system.