The distribution of consecutive primes is surprisingly erratic, with different patterns occurring with wildly different frequencies, due to secondary terms slowly tending to zero.

Unexpected biases in the distribution of consecutive primes

This paper presents a new mathematical formula for calculating prime numbers for all integers, improving the accuracy of previous formulae and addressing the limitations of previous methods.

Advanced Mathematical Formulas to Calculate Prime Numbers

This paper presents a squaring prime pattern, fifteen different types of primes, and prime factorization analysis, which is crucial for cryptographic encryption systems and various real-life applications.

A Review of Prime Numbers, Squaring Prime Pattern, Different Types of Primes and Prime Factorization Analysis

The Alfa Prime Theory and Alfa Prime Series provide a new method to find prime numbers and their prime factors, highlighting the additive property of natural numbers and its impact on finding prime and composite numbers and their prime factors.

Prime Number Theory & New Method to Find Prime Numbers & Prime Factors

This article has solved the prime number problem, allowing us to determine the biggest prime numbers compared to our machines' capacity, promoting information technology security and promoting the NTIC.

The Prime Numbers

Newmann's proof of the prime number theorem demonstrates the asymptotic behavior of positive prime numbers using the Riemann zeta function.

A Survey on Newmann’s proof of the prime number theorem

This paper presents Python programs to generate prime numbers, analyze their role in cryptography and cicada, and explore their applications in various platforms and algorithms.

Prime numbers and their analysis

Prime numbers play a crucial role in modern mathematics, but are largely absent from school curricula, despite their importance in banking and security.

Is there a greater role for prime numbers in our schools

The Riemann zeta function may provide a key to understanding complex atomic systems and break a longtime mathematical logjam, potentially leading to a proof of a century-old problem.

Prime Formula Weds Number Theory and Quantum Physics

This study presents an innovative approach to prime numbers, using a modified Chi-square function and approximate inductive algorithms to find the approximate value of a prime Pn+1 from the previous Pn.

Computer Simulation Model of Prime Numbers

Prime numbers exhibit a mixture of order and chaos, with some patterns and regular distributions, but no deterministic formula for generating large numbers guaranteed to be prime.

Structure and Randomness in the Prime Numbers

This paper presents a deterministic computational algorithm that reduces the number of operations in calculating the prime number counting function, (x), by excluding multiples of 3.

Counting prime numbers in arithmetic sequences

This chapter provides an overview of algebraic number theory, focusing on primes and prime decompositions, and introduces key concepts and ideas in the field.

Primes and Algebraic Number Theory

Number theory has significant applications in computational science and cryptography, particularly in RSA encryption, which is the most widely used encryption technique today.

NUMBER THEORY AND THEIR APPLICATION IN COMPUTER SCIENCE AND CRYPTOGRAPHY

This paper proposes a simple elimination method for identifying and predicting prime numbers using a simple separation scheme.

Order of Integer Numbers and Structure of Prime Numbers

This paper estimates the number of primes in sparse polynomial sequences, x + 2y, where y is small, and shows that the number of such primes is limited by the number of x + 2y primes in the sequence.

Prime values of a sparse polynomial sequence

Number theory explores the relationship between integers, prime numbers, squares and cubes, and perfect numbers, addressing questions such as how long gaps between prime numbers can be, the formula for producing perfect numbers, and which primes can be expressed as sums of squares.

1. What is number theory?

Additive prime number theory focuses on representing integers as sums of primes, with the central problem being to prove or refute Goldbach's conjecture that every even integer 4 can be represented as the sum of 2 primes.

Additive Prime Number Theory

This new theory provides a unique relationship to find the prime numbers, solving the long-standing problem of finding a general formula for them.

Unique Relationship to Find The Prime Numbers (New Theory)

What is the significance of prime numbers and number theory?

These studies suggest that prime numbers and number theory are significant for understanding the distribution of primes, developing new mathematical formulas, enhancing cryptographic systems, improving information technology security, and potentially solving longstanding mathematical problems.