Discussion on Astronomical Prime Numbers and Re-evaluating the Primali

[Charles Kusniec]

Subject: Discussion on Astronomical Prime Numbers and Re-evaluating the Primality of the Number 1

Dear Members of the Physics Forum,

I hope this message finds you well. I've been avidly exploring various discussions on prime numbers and came across an intriguing thread on your forum titled "Is This Simple Algorithm the Key to Finding the Next Largest Prime Number?" ([Physics Forums Thread](https://www.physicsforums.com/threads/is-this-simple-algorithm-the-key-to-finding-the-next-largest-prime-number.843519/)). This discussion, coupled with insights from post #27 of the thread at the Mersenne Forum ([Mersenne Forum Thread](https://www.mersenneforum.org/showthread.php?t=27328&page=3)), has prompted me to propose a novel approach to identifying Astronomical Prime Numbers of any size.

Central to my approach is a reconsideration of the primality status of the number 1. Traditional mathematical conventions exclude 1 from the set of prime numbers. However, I believe that redefining 1 as a prime number could offer new perspectives and methodologies in prime number theory, particularly in the context of searching for extremely large prime numbers.

This idea, admittedly, challenges long-established norms in number theory. Yet, it opens a gateway to potentially groundbreaking techniques in identifying large primes, a topic of immense interest not only for its mathematical elegance but also for its practical applications in fields such as cryptography.

I am keen on discussing this concept further with the esteemed members of this forum. Your insights, critiques, and contributions would be invaluable in exploring the feasibility and implications of this approach. If this topic resonates with your interests, I would be honored to initiate a detailed discussion here.

Looking forward to an engaging and enlightening exchange of ideas.

Best regards,

 

[PeroK]

Whether we consider 1 as a prime number or not is of no significance whatsoever.

 

[Hornbein]

Whether we consider 1 as a prime number or not is of no significance whatsoever.

If one were a prime number then all numbers would be composite, including one. There would be no prime numbers.

 

[PeroK]

If one were a prime number then all numbers would be composite, including one. There would be no prime numbers.

One is not a prime number by convention (in modern mathematics). There's a discussion on the history of the primality of one here:

https://en.wikipedia.org/wiki/Prime_number

 

[berkeman]

Thread is closed for Moderation...

 

[fresh_42]

If we allowed units to be prime, then the concept of prime ideals in general and prime numbers in particular would become void. Units fulfill the primality condition trivially since they "divide" any number. Excluding units is of vital importance to work with primes in a meaningful way.

This thread will remain closed since ...

• ... the debate of personal theories is against our rules,
• ... it is based on unreasonable assumptions,
• ... factorization (UPD) is as of current knowledge NP-hard,
• ... if UPD was in P, then I'd smell a Fields medal lying around,
• ... and it is extremely unlikely that this would happen on the internet.