The gaps between the gaps: some patterns in the prime number sequence

2004 ◽  
Vol 341 ◽  
pp. 607-617 ◽  
Author(s):  
George G Szpiro
Keyword(s):  
Prime Number ◽  
Number Sequence

RNA Structure Based on Prime Number Sequence

1995 ◽  
pp. 42-43
Author(s):  
Mels Sluyser ◽  
Erik L. L. Sonnharnmer
Keyword(s):  
Prime Number ◽  
Rna Structure ◽  
Number Sequence

scholarly journals SAVINGS TIME EXECUTION PRIMA NUMBERS GENERATOR USING BIT-ARRAY STRUCTURE

2021 ◽  
Vol 1 (1) ◽  
pp. 20-27
Author(s):  
Letnan Kolonel Elektronika Imat Rakhmat Hidayat, S.T., M.Eng
Keyword(s):  
Prime Number ◽  
Execution Time ◽  
Computing Time ◽  
Hash Table ◽  
Research Data ◽  
Number Sequence ◽  
Pattern Sequence ◽  
Size Measure ◽  
Use Efficiency ◽  
Time Savings

Prime number in growth computer science of number theory and very need to yield an tool which can yield an hardware storey level effectiveness use efficiency and Existing Tools can be used to awaken regular prime number sequence pattern, structure bit-array represent containing subdividing variables method of data aggregate with every data element which have type of equal, and also can be used in moth-balls the yielded number sequence. Prime number very useful to be applied by as bases from algorithm kriptografi key public creation, hash table, best algorithm if applied hence is prime number in order to can minimize collision (collisions) will happen, in determining pattern sequence of prime number which size measure is very big is not an work easy to, so that become problems which must be searched by the way of quickest to yield sequence of prime number which size measure is very big Serial use of prosesor in seeking sequence prime number which size measure is very big less be efficient remember needing of computing time which long enough, so also plural use prosesor in seeking sequence of prime number will concerning to price problem and require software newly. So that by using generator of prime number use structure bit-array expected by difficulty in searching pattern sequence of prime number can be overcome though without using plural processor even if, as well as time complexity minimization can accessed. Execution time savings gained from the research seen from the research data, using the algorithm on the input Atkins 676,999,999. 4235747.00 execution takes seconds. While the algorithm by using an array of input bits 676,999,999. 13955.00 execution takes seconds. So that there is a difference of execution time for 4221792.00 seconds.

The first-digit frequencies of prime numbers and Riemann zeta zeros

2009 ◽  
Vol 465 (2107) ◽  
pp. 2197-2216 ◽  
Author(s):  
Bartolo Luque ◽  
Lucas Lacasa
Keyword(s):  
Prime Number ◽  
Final Analysis ◽  
Prime Number Theorem ◽  
Prime Numbers ◽  
Number Sequence ◽  
Riemann Zeta ◽  
Global Patterns ◽  
Digit Frequencies ◽  
Ultimate Nature ◽  
Shed Light

Prime numbers seem to be distributed among the natural numbers with no law other than that of chance; however, their global distribution presents a quite remarkable smoothness. Such interplay between randomness and regularity has motivated scientists across the ages to search for local and global patterns in this distribution that could eventually shed light on the ultimate nature of primes. In this paper, we show that a generalization of the well-known first-digit Benford's law, which addresses the rate of appearance of a given leading digit d in datasets, describes with astonishing precision the statistical distribution of leading digits in the prime number sequence. Moreover, a reciprocal version of this pattern also takes place in the sequence of the non-trivial Riemann zeta zeros. We prove that the prime number theorem is, in the final analysis, responsible for these patterns.

The Natural Numbers

2018 ◽  
Author(s):  
Øystein Linnebo
Keyword(s):  
Natural Number ◽  
Peano Arithmetic ◽  
Number Sequence ◽  
Natural Numbers ◽  
Ordinal Numbers ◽  
Cardinal Numbers

How are the natural numbers individuated? That is, what is our most basic way of singling out a natural number for reference in language or in thought? According to Frege and many of his followers, the natural numbers are cardinal numbers, individuated by the cardinalities of the collections that they number. Another answer regards the natural numbers as ordinal numbers, individuated by their positions in the natural number sequence. Some reasons to favor the second answer are presented. This answer is therefore developed in more detail, involving a form of abstraction on numerals. Based on this answer, a justification for the axioms of Dedekind–Peano arithmetic is developed.

Largest fake prime number weighs in at 300 billion digits

2013 ◽  
Vol 217 (2904) ◽  
pp. 14
Author(s):  
Jacob Aron
Keyword(s):  
Prime Number

scholarly journals Deep ConvNet: Non-Random Weight Initialization for Repeatable Determinism, Examined with FSGM

Sensors ◽  
2021 ◽  
Vol 21 (14) ◽  
pp. 4772
Author(s):  
Richard N. M. Rudd-Orthner ◽  
Lyudmila Mihaylova
Keyword(s):  
Cross Validation ◽  
Color Image ◽  
Validation Dataset ◽  
Number Sequence ◽  
Random Weight ◽  
Fast Gradient ◽  
Weight Initialization ◽  
Fitting In ◽  
Sequence Substitution ◽  
Sign Method

A repeatable and deterministic non-random weight initialization method in convolutional layers of neural networks examined with the Fast Gradient Sign Method (FSGM). Using the FSGM approach as a technique to measure the initialization effect with controlled distortions in transferred learning, varying the dataset numerical similarity. The focus is on convolutional layers with induced earlier learning through the use of striped forms for image classification. Which provided a higher performing accuracy in the first epoch, with improvements of between 3–5% in a well known benchmark model, and also ~10% in a color image dataset (MTARSI2), using a dissimilar model architecture. The proposed method is robust to limit optimization approaches like Glorot/Xavier and He initialization. Arguably the approach is within a new category of weight initialization methods, as a number sequence substitution of random numbers, without a tether to the dataset. When examined under the FGSM approach with transferred learning, the proposed method when used with higher distortions (numerically dissimilar datasets), is less compromised against the original cross-validation dataset, at ~31% accuracy instead of ~9%. This is an indication of higher retention of the original fitting in transferred learning.

scholarly journals Sign changes in the prime number theorem

2021 ◽  
Author(s):  
Thomas Morrill ◽  
Dave Platt ◽  
Tim Trudgian
Keyword(s):  
Prime Number ◽  
Prime Number Theorem ◽  
Sign Changes

3126. A Prime Number Conjecture

1965 ◽  
Vol 49 (369) ◽  
pp. 299
Author(s):  
T. Mitsopoulos
Keyword(s):  
Prime Number

Pointwise bound for ℓ-torsion in class groups: Elementary abelian extensions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Jiuya Wang
Keyword(s):  
Galois Group ◽  
Prime Number ◽  
Finite Groups ◽  
Upper Bound ◽  
Abelian Groups ◽  
Class Groups ◽  
Abelian Extensions ◽  
Pointwise Bound ◽  
First Case

AbstractElementary abelian groups are finite groups in the form of {A=(\mathbb{Z}/p\mathbb{Z})^{r}} for a prime number p. For every integer {\ell>1} and {r>1}, we prove a non-trivial upper bound on the {\ell}-torsion in class groups of every A-extension. Our results are pointwise and unconditional. This establishes the first case where for some Galois group G, the {\ell}-torsion in class groups are bounded non-trivially for every G-extension and every integer {\ell>1}. When r is large enough, the unconditional pointwise bound we obtain also breaks the previously best known bound shown by Ellenberg and Venkatesh under GRH.

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