Related papers: Using Repeating Decimals As An Alternative To Prim…
This article is meant to provide an additional point of view, applying known knowledge, to supply keys that have a series of non-repeating digits, in a manner that is not usually thought of. Traditionally, prime numbers are used in…
The chronicle of prime numbers travel back thousands of years in human history. Not only the traits of prime numbers have surprised people, but also all those endeavors made for ages to find a pattern in the appearance of prime numbers has…
A cryptarithm (or alphametic) is a mathematical puzzle in which numbers are represented with words in such a way that identical letters stand for equal digits and distinct letters for unequal digits. An alphametic puzzle is usually given in…
It is possible to interpret text as numbers (and vice versa) if one interpret letters and other characters as digits and assume that they have an inherent immutable ordering. This is demonstrated by the conventional digit set of the…
This paper investigates the length of the repeating decimal part when a fraction is expressed in decimal form. First, it provides a detailed explanation of how to calculate the length of the repeating decimal when the denominator of the…
We investigate secret key rates for the quantum repeater using encoding [L. Jiang et al., Phys. Rev. A 79, 032325 (2009)] and compare them to the standard repeater scheme by Briegel, D\"ur, Cirac, and Zoller. The former scheme has the…
We present a new sieve that allows us to find the prime numbers by using only regular patterns and, more importantly, avoiding any duplication of elements between them.
This article proposes the use of pseudorandom decimal sequences that have gone through an additional random mapping for the design of cryptographic keys. These sequences are generated by starting with inverse prime expansions in base 3 and…
This paper introduces a binary encoding that supports arbitrarily large, small and precise decimals. It completely preserves information and order. It does not rely on any arbitrary use-case-based choice of calibration and is readily…
We create a simple test for distinguishing between sets of primes and random numbers using just the sum-of-digits function. We find that the sum-of-the-digits of prime numbers does not have an equal probability of being odd or even. The…
New exceptional (i.e. non-repeating) prime number multiplets are given and formulated in terms of arithmetic progressions, along with laws governing them. Accompanying repeating prime number multiplets are pointed out. Prime number…
This paper presents a novel approach at the intersection of machine learning and number theory, focusing on the classification of prime and non-prime numbers. At the core of our research is the development of a highly sparse encoding…
We had recently shown that every positive integer can be represented uniquely using a recurrence sequence, when certain restrictions on the digit strings are satisfied. We present the details of how such representations can be used to build…
Non-uniquely decodable codes can be defined as the codes that cannot be uniquely decoded without additional disambiguation information. These are mainly the class of non-prefix-free codes, where a codeword can be a prefix of other(s), and…
This paper proposes the use of the binary primes sequence to strengthen pseudorandom (PN) decimal sequences for cryptography applications. The binary primes sequence is added to the PN decimal sequence (where one can choose from many…
Prime reciprocals have applications in coding and cryptography and for generation of random sequences. This paper investigates the structural redundancy of prime reciprocals in base 10 in a manner that parallels an earlier study for binary…
The prime numbers look like a randomly chosen sequence of natural numbers, but there is still no strict theory to determine 'Randomness'. In these years, cryptography has developed a battery of statistical tests for randomness. In this…
In database design, Composite Keys are used to uniquely identify records and prevent data duplication. However, they require more memory and storage space than single keys, and can make queries more CPU-intensive. Surrogate Keys are an…
A compression algorithm is presented that uses the set of prime numbers. Sequences of numbers are correlated with the prime numbers, and labeled with the integers. The algorithm can be iterated on data sets, generating factors of doubles on…
Prime numbers are one of the most intriguing figures in mathematics. Despite centuries of research, many questions remain still unsolved. In recent years, computer simulations are playing a fundamental role in the study of an immense…