Innovating Primes: How the Prime Heart Theorem Could Change Everything

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Execution time: 0.05596423149108887 seconds.
All Primes, Imagine developing a key to mastering prime computation: build the prime you want, the way you want it. Harness control over prime numbers effortlessly.

 

In each of these primes, you can observe that the sequence 840792690619648459681960002881(which is also prime) is consistently embedded within all the listed numbers. This allows us to systematically explore the generation of primes by modifying the surrounding digits, offering a potentially useful tool for cryptographic key generation or theoretical research in prime computation. The goal is to harness more control over prime number generation, making it more predictable and tailored, which could revolutionize certain aspects of cryptography or mathematical research

 

With greater precision in my query, I seek to understand if a mathematical framework exists that can adeptly identify all prime numbers in the vicinity of a given numerical value, such as 125,468,923, within a defined range of [-10,000, +10,000]. The emphasis is on an approach that eschews the exhaustive examination of every number within this span, potentially harnessing a more nuanced strategy for prime identification. I am genuinely interested in insights into such methodologies

 

Suppose you had a mathematical construct of the following...

All numbers are composed of a numerical quantity, and a dimensional quantity.
Zero is the absence of a numerical quantity, but is a single dimensional quantity.
Multiplication, and division are adapted accordingly.
There are varying quantities of zero.
Division by zero is defined.

Would such a construct help you in your calculations of primes? Consider perhaps philosophically, that there now is a relationship between a numbers "value", and its "space". I truly hope that this might be of help!