- #1
rrronny
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Let [tex]\mathbb{P}[/tex] the set of primes. Let's [tex]p,q \in \mathbb{P}[/tex] and [tex]p \le q.[/tex] Find the pairs [tex](p,q)[/tex] such that [tex]2^p+3^q[/tex] and [tex]2^q+3^p[/tex] are simultaneously primes.
Hi Borek,Borek said:You have to show your attempts to receive help. This is a forum policy.
quantumdoodle said:wait... 6 is not a prime...
Sorry... I meant the sixth prime number.quantumdoodle said:wait... 6 is not a prime...
"On the primality of 2^p+3^q" is a highly studied and debated topic in mathematics, specifically in the field of number theory. It explores the properties and patterns of numbers in the form of 2^p+3^q, where p and q are prime numbers. This topic is important because it has implications for understanding the distribution of prime numbers and their relationship with other mathematical concepts.
The formula 2^p+3^q is a form of a prime-generating polynomial, meaning that it generates prime numbers for certain values of p and q. This formula has been extensively studied by mathematicians to understand its properties and potential patterns in the generation of prime numbers.
As of now, there is no known general rule or pattern for determining the primality of 2^p+3^q. It is a highly complex mathematical problem that is still being actively researched by mathematicians. However, there have been some significant discoveries and conjectures about the behavior of this formula.
Understanding the primality of 2^p+3^q has potential applications in cryptography, as it is closely related to the security of certain encryption algorithms. It also has implications for understanding the distribution of prime numbers and their relationship with other mathematical concepts, which can lead to further advancements in number theory and other fields of mathematics.
As of now, the primality of 2^p+3^q cannot be proven for all values of p and q. However, there have been some significant discoveries and conjectures about the behavior of this formula that have been proven to hold true for certain values. The search for a proof of its primality for all values continues to be an active area of research in mathematics.