Function for Prime Numbers

The function [5*(1+1/x) + 1]

for each value of x determined by Sequence A

x = (5²)+5*2*(n(n+1)/2)

where n ≥ 0

determines an infinite series of fractional numbers N/d:

5*(1+1/x) + 1 = N/d

such that N and d are prime numbers.

This function, when applied to specific subsets of Sequence A, quickly identifies a significant quantity of prime numbers, including those with thousands of digits.

Algorithms developed based on this function have demonstrated extraordinary efficiency, finding numerous prime numbers with hundreds or thousands of digits in minutes or even seconds.

All results were obtained using a 2020 MacBook Pro, equipped with a 2 GHz quad-core Intel Core i5 processor, Intel Iris Plus Graphics 1536 MB, and 16 GB of 3733 MHz LPDDR4X memory, fully utilizing the available computational resources.

The use of much more powerful supercomputers would enable the algorithm, based on this function and specific subsets of Sequence A or fractional subsets, to find prime numbers with hundreds of millions or even billions of digits.

This work has the potential to revolutionize the field of number theory, offering practical applications of great relevance, such as advanced cryptography.

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