SYSTEM AND METHOD FOR EFFICIENT PRIME NUMBER GENERATION AND VERIFICATION

Abstract

Disclosed is a system for generating and verifying prime numbers, comprising a processing unit performing arithmetic operations to generate prime numbers. A memory unit stores candidate values and previously computed prime numbers. A prime-checking component assesses primality by evaluating divisibility using a predefined set of prime factors. A random number generator produces candidate values within a defined range, and a verification component compares computed prime numbers against a predefined verification criterion. An output unit provides a list of validated prime numbers upon successful verification. A control unit manages interactions among the processing unit, prime-checking component, random number generator, verification component, and output unit to enable prime number generation and verification.

Specification

Description:Field of the Invention


The present disclosure generally relates to computational systems. Further, the present disclosure particularly relates to systems for prime number generation and verification.
Background
The background description includes information that may be useful in understanding the present invention. It is not an admission that any of the information provided herein is prior art or relevant to the presently claimed invention, or that any publication specifically or implicitly referenced is prior art.
Computational generation and verification of prime numbers constitute essential functions in numerous fields, particularly within cryptography and digital security. Prime numbers serve as the foundation for many cryptographic protocols, such as public-key cryptography, due to their unique properties. Efficient and reliable generation and verification of prime numbers are thus critical in ensuring secure data transmission, secure storage, and validation processes. Over time, various methods have been developed to generate prime numbers and assess the primality of candidate numbers.
Conventional methods for generating prime numbers frequently rely on sequential and deterministic approaches, which incrementally examine each integer to verify its primality. One well-known method involves trial division, where each candidate number undergoes sequential testing for divisibility by smaller prime numbers. However, as the range of desired prime numbers increases, trial division often becomes computationally intensive and inefficient. Although such methods are widely implemented, they generally require substantial computational resources, particularly when examining large integers, thereby limiting practical applications within systems where processing efficiency is paramount.
Another conventional method to verify prime numbers involves probabilistic testing techniques, such as the Miller-Rabin primality test. This test operates by evaluating candidate numbers based on certain probabilistic criteria, which enables rapid identification of non-prime candidates. Although probabilistic testing offers computational benefits by reducing processing times, these tests cannot conclusively verify primality and instead indicate a high probability that a number is prime. Consequently, probabilistic methods introduce uncertainty into the verification process, which can be unsuitable for systems demanding absolute certainty in prime verification.
Further advancements in prime number generation techniques have incorporated pseudorandom number generators to expedite the candidate selection process. Such techniques involve generating random or pseudorandom numbers within a specified range, which are subsequently evaluated for primality. However, the effectiveness of pseudorandom number generation techniques remains limited by the non-uniform distribution of primes across the number spectrum. Randomly selected candidate numbers frequently result in non-prime numbers, thereby requiring additional computational resources for multiple verification attempts. This approach, while beneficial for some applications, fails to balance efficiency and accuracy adequately, particularly for large-scale prime generation.
Additionally, other methods have utilized caching systems to store previously computed prime numbers or candidate values to optimize processing efficiency. By referencing stored prime numbers, these caching systems reduce repetitive calculations for commonly encountered numbers during prime generation. Nonetheless, caching solutions are often constrained by storage limitations, particularly when handling high volumes of data, resulting in reduced scalability and potential delays in prime verification. Moreover, retrieval of cached data may contribute to latency, impacting the overall system efficiency in applications requiring rapid prime generation and verification.
Parallel processing frameworks have also been introduced within conventional systems to divide candidate numbers into smaller segments and evaluate each segment concurrently. While parallel processing increases the overall speed of prime generation, such techniques encounter issues with data synchronization and coordination among multiple processing units, which may introduce delays and inconsistencies. Furthermore, the requirement for specialized hardware to support parallel processing configurations may restrict applicability to certain system environments, particularly within constrained computational architectures.
In light of the above discussion, there exists an urgent need for solutions that overcome the problems associated with conventional systems and techniques for prime number generation and verification.
Summary
The following presents a simplified summary of various aspects of this disclosure in order to provide a basic understanding of such aspects. This summary is not an extensive overview of all contemplated aspects, and is intended to neither identify key or critical elements nor delineate the scope of such aspects. Its purpose is to present some concepts of this disclosure in a simplified form as a prelude to the more detailed description that is presented later.
The following paragraphs provide additional support for the claims of the subject application.
An objective of the present disclosure is to provide a system and method that enables efficient generation and verification of prime numbers. Such a system aims to reduce computational load and processing time, thereby optimizing the selection and validation of prime numbers for various applications.
In an aspect, the present disclosure provides a system comprising a processing unit that performs arithmetic operations to generate prime numbers. A memory unit stores candidate values and previously computed prime numbers. A prime-checking component assesses primality by applying divisibility tests based on a predefined set of prime factors, and a random number generator selects candidate values from a defined range. A verification component compares computed prime numbers against verification criteria, while an output unit displays validated prime numbers. A control unit manages the interactions among said components to enable the efficient generation and verification of prime numbers.
Furthermore, the system achieves an efficient verification process by reducing repetitive calculations through the caching of prior results, increasing candidate diversity using a non-linear sequence generator, and expediting computations via parallel processing. An adaptive threshold adjuster dynamically modifies selection parameters, and an error detection unit enhances reliability. Additionally, a reporting unit analyzes prime distributions, thereby extending potential applications of the system.

Brief Description of the Drawings


The features and advantages of the present disclosure would be more clearly understood from the following description taken in conjunction with the accompanying drawings in which:
FIG. 1 illustrates a system for generating and verifying prime numbers, in accordance with the embodiments of the present disclosure.
FIG. 2 illustrates a flowchart of the structured method for generating and verifying prime numbers, in accordance with the embodiments of the present disclosure.
Detailed Description
In the following detailed description of the invention, reference is made to the accompanying drawings that form a part hereof, and in which is shown, by way of illustration, specific embodiments in which the invention may be practiced. In the drawings, like numerals describe substantially similar components throughout the several views. These embodiments are described in sufficient detail to claim those skilled in the art to practice the invention. Other embodiments may be utilized and structural, logical, and electrical changes may be made without departing from the scope of the present invention. The following detailed description is, therefore, not to be taken in a limiting sense, and the scope of the present invention is defined only by the appended claims and equivalents thereof.
The use of the terms "a" and "an" and "the" and "at least one" and similar referents in the context of describing the invention (especially in the context of the following claims) are to be construed to cover both the singular and the plural, unless otherwise indicated herein or clearly contradicted by context. The use of the term "at least one" followed by a list of one or more items (for example, "at least one of A and B") is to be construed to mean one item selected from the listed items (A or B) or any combination of two or more of the listed items (A and B), unless otherwise indicated herein or clearly contradicted by context. The terms "comprising," "having," "including," and "containing" are to be construed as open-ended terms (i.e., meaning "including, but not limited to,") unless otherwise noted. Recitation of ranges of values herein are merely intended to serve as a shorthand method of referring individually to each separate value falling within the range, unless otherwise indicated herein, and each separate value is incorporated into the specification as if it were individually recited herein. All methods described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The use of any and all examples, or exemplary language (e.g., "such as") provided herein, is intended merely to better illuminate the invention and does not pose a limitation on the scope of the invention unless otherwise claimed. No language in the specification should be construed as indicating any non-claimed element as essential to the practice of the invention.
Pursuant to the "Detailed Description" section herein, whenever an element is explicitly associated with a specific numeral for the first time, such association shall be deemed consistent and applicable throughout the entirety of the "Detailed Description" section, unless otherwise expressly stated or contradicted by the context.
As used herein, the term "processing unit" refers to any computational component capable of performing arithmetic and logical operations associated with prime number generation. The processing unit may perform operations that include generating candidate numbers, initiating arithmetic tests for assessing candidate numbers, and interacting with various other components within the system to facilitate prime number generation and verification. The processing unit may consist of single or multiple processors, cores, or computational segments that collectively enable high-speed execution of arithmetic operations. Additionally, the processing unit may function as a central hub, coordinating data processing activities and managing workloads across other connected components to support efficient and systematic prime number generation. Furthermore, the processing unit may dynamically adjust its computational speed or arithmetic precision based on input from other system components to maintain an optimal operational balance between processing efficiency and accuracy in prime number generation.
As used herein, the term "memory unit" refers to a storage device operatively connected to the processing unit for storing candidate values and previously computed prime numbers. The memory unit may include volatile or non-volatile storage types, such as RAM, ROM, flash memory, or other appropriate data storage technologies, to retain data necessary for prime number computations and verification processes. The memory unit may further store intermediate results from arithmetic operations, enabling efficient access and retrieval during subsequent computations. Additionally, the memory unit may provide cached access to previously generated prime numbers, thereby reducing redundant calculations and enhancing processing efficiency for prime number assessments. Moreover, the memory unit may also support systematic data retrieval and storage functionalities, ensuring that prime number computations are sustained without unnecessary delays caused by memory constraints.
As used herein, the term "prime-checking component" refers to a component connected to the processing unit that assesses the primality of candidate values by evaluating divisibility based on a set of prime factors. The prime-checking component may include various arithmetic elements that sequentially or concurrently test divisibility properties within each candidate number. The prime-checking component may use a predetermined set of prime factors or customizable factor groups to filter non-prime candidates, thereby increasing efficiency in the selection of prime numbers. Additionally, the prime-checking component may also perform computations such as modular arithmetic or divisibility testing across multiple candidate numbers, and may interface with other components to verify accuracy of assessments before further processing. The prime-checking component may also adaptively optimize its divisibility checks based on predefined configurations or historical performance metrics.
As used herein, the term "random number generator" refers to a generator that produces candidate values within a specified range and transmits said candidate values to the processing unit for further assessment. The random number generator may use a defined range and randomization method to produce unique values and maintain diversity among the generated candidate numbers, thus supporting an unbiased and systematic approach to prime number selection. Furthermore, the random number generator may produce values based on non-linear sequences, ensuring that each candidate number introduced for assessment is distinct from previously generated values. Additionally, the random number generator may support randomization techniques suitable for prime number selection and enable the exclusion of specific values from the candidate pool based on custom criteria. Such generator may also vary its range dynamically based on adjustments made by other system components.
As used herein, the term "verification component" refers to a component responsible for verifying computed prime numbers by comparing them against a predefined verification criterion. The verification component may incorporate methods for cross-verification, such as comparing results with standardized criteria or employing probabilistic testing techniques, to confirm the primality of each validated candidate number. The verification component may also assess results from the prime-checking component and other system components to ensure accuracy and consistency of prime number verification. Furthermore, the verification component may execute re-verification of prime numbers through additional test cycles or alternative criteria when necessary. Additionally, the verification component may allow for modifications to the verification criterion based on system configurations or specific prime number requirements, thereby enabling flexible prime number verification based on application needs.
As used herein, the term "output unit" refers to a component responsible for generating and displaying a list of validated prime numbers upon successful verification of primality by the verification component. The output unit may receive verified data directly from the verification component and present the prime numbers in a structured format suitable for further computational or analytical applications. Additionally, the output unit may employ visualization methods, such as tables, graphs, or plots, to represent prime number distributions or properties based on user-defined criteria. Furthermore, the output unit may also interface with external systems or devices to transmit the list of validated prime numbers for external use. In certain configurations, the output unit may offer multiple output formats to enable compatibility with different end-use requirements, allowing users to select output types that best meet specific needs.
As used herein, the term "control unit" refers to a management component responsible for coordinating interactions between the processing unit, prime-checking component, random number generator, verification component, and output unit. The control unit may function as the central administrative component within the system, directing communication and task distribution among connected components. The control unit may monitor operational parameters such as execution times, processing load, or computation status to maintain system stability. Additionally, the control unit may adjust component configurations based on performance metrics to balance efficiency and accuracy in prime number generation and verification. Furthermore, the control unit may implement timing mechanisms that optimize the order and priority of component operations, while also enabling adjustments to candidate ranges and verification criteria in response to user-defined parameters or application needs.
FIG. 1 illustrates a system for generating and verifying prime numbers, in accordance with the embodiments of the present disclosure. In an embodiment, a processing unit performs arithmetic operations associated with prime number generation. Processing unit may execute arithmetic and logical operations needed to generate candidate values, conduct divisibility tests, and interact with other components for seamless integration within the prime number generation system 100. Processing unit may contain one or more processors, cores, or logical partitions that enable high-speed execution and prioritization of arithmetic operations. Processing unit may perform mathematical operations such as modular arithmetic, factorization, or remainder calculations, supporting rapid identification of candidate numbers. Additionally, processing unit may dynamically manage workload distribution by allocating computational resources based on system demand, thereby facilitating balanced performance and operational efficiency across multiple tasks. Processing unit may interact with memory unit to retrieve previously stored prime numbers or candidate values and with prime-checking component to evaluate divisibility tests or factor-based assessments. Processing unit may also perform self-monitoring to optimize its operational parameters, adjusting clock speed or core allocation based on input from control unit . Processing unit may further execute instructions that optimize arithmetic precision and limit redundant calculations, contributing to reliable and efficient prime number generation.
In an embodiment, memory unit is operatively connected to processing unit to store candidate values and previously computed prime numbers. Memory unit may include volatile or non-volatile storage such as RAM, ROM, flash memory, or other suitable data storage configurations. Memory unit supports the efficient storage and retrieval of data required for prime number generation, including caching intermediate results from prior computations. Memory unit may additionally provide fast access to previously verified prime numbers, thus preventing repetitive calculations and enabling processing unit to access verified data for expedited processing. Memory unit may also incorporate dedicated caching mechanisms, allowing retention of frequently accessed values, and optimizing data retrieval. Memory unit supports systematic storage protocols, ensuring organized retention of candidate values, prime numbers, and divisibility assessments for access by connected components such as prime-checking component and verification component . Memory unit may maintain a predefined storage structure, allowing efficient organization of data that facilitates prime number generation.
In an embodiment, a prime-checking component is connected to processing unit to assess the primality of candidate values by evaluating divisibility based on a set of prime factors. Prime-checking component performs arithmetic operations that test candidate values for divisibility against predetermined factors to determine primality. Prime-checking component may implement sequential or concurrent factor evaluations, either testing individual candidates one-by-one or processing multiple candidates simultaneously. Prime-checking component may use an array of prime divisors stored within memory unit or other pre-defined factors to filter non-prime values efficiently. Prime-checking component may also apply modular arithmetic tests to expedite divisibility checks. Prime-checking component may further interface with processing unit to conduct detailed assessments and use available computational resources for high-speed evaluations. The component may vary divisibility checks, selecting prime factors based on system-configured criteria to optimize accuracy in filtering out non-prime numbers.
In an embodiment, a random number generator is connected to processing unit to produce candidate values within a defined range for prime number evaluation. Random number generator may generate candidate values within a configurable numerical range based on system parameters, providing an initial pool of values for prime-checking component . Random number generator may apply a non-linear sequence or other randomization technique to ensure the diversity of candidate values, which prevents predictability and facilitates unbiased prime selection. Random number generator may additionally restrict certain ranges based on criteria defined by control unit , thereby refining the candidate pool for more efficient processing. Random number generator interacts with memory unit to confirm that generated values align with predefined selection parameters and avoids generating previously computed values to maintain uniqueness among candidates. The generator may also dynamically adjust its output range based on system demand, supporting adaptive and efficient prime number generation.
In an embodiment, a verification component compares computed prime numbers against a predefined verification criterion to confirm their primality. Verification component may implement deterministic or probabilistic criteria to ensure the integrity of verified prime numbers before such values proceed to output unit. Verification component receives results from prime-checking component, analyzing whether candidate numbers meet established verification standards. Verification component may employ iterative or probabilistic tests to validate the prime status of each candidate, ensuring reliability in the generation process. Additionally, verification component may interface with memory unit , cross-referencing verification results against stored prime numbers to detect and eliminate duplicates. Verification component may conduct multiple verification cycles based on system-defined accuracy requirements. Verification component may further coordinate with control unit to modify or refine verification criteria based on evolving system configurations, providing flexible validation of candidate numbers.
In an embodiment, an output unit generates and displays a list of validated prime numbers upon successful verification of primality by verification component . Output unit may receive and display final results in various formats, such as text lists, tables, or graphical visualizations, to convey validated prime numbers for further use. Output unit may interact with memory unit and verification component, ensuring that only verified and non-duplicative prime numbers are displayed. Output unit may also interface with external systems or devices, enabling the transmission of validated prime numbers for computational or analytical applications outside of system 100. Additionally, output unit may allow users to define specific display preferences, such as list formats, visual arrangements, or other customization parameters that align with system requirements. Output unit may support multi-format output options, adapting displayed data to meet end-use needs.
In an embodiment, a control unit manages interactions between processing unit , prime-checking component , random number generator , verification component , and output unit to facilitate efficient prime number generation and verification. Control unit operates as the central coordinating entity, monitoring operational parameters such as processing load, execution timing, and data throughput to optimize system performance. Control unit may implement task prioritization strategies, distributing workloads among connected components to maintain balanced system functionality. Additionally, control unit may interface with processing unit to regulate computational resources, adjusting processing parameters dynamically based on system demand. Control unit may also synchronize operations between random number generator and verification component to ensure timely generation, assessment, and validation of candidate values. Control unit may modify criteria, such as divisibility thresholds or verification standards, based on evolving computational requirements, thereby supporting flexible and adaptive prime number generation and verification.
In an embodiment, the prime-checking component comprises a divisibility test unit configured to filter non-prime numbers by leveraging the properties of modular arithmetic. This divisibility test unit examines each candidate number by testing for divisibility using a predefined set of smaller prime factors, effectively removing non-prime numbers from the selection pool. The divisibility test unit may perform modular operations, evaluating whether a candidate number produces a remainder when divided by one of the predefined sets of prime divisors. By applying modular arithmetic in this way, the divisibility test unit efficiently eliminates candidate values that do not meet the criteria for prime numbers, thus reducing the quantity of candidates that require further verification. Additionally, the divisibility test unit may use adaptive divisor sets that vary based on the size of candidate values or on the prime ranges of interest within the system. The divisibility test unit may also interact with memory unit to access stored prime divisors or candidate numbers and may coordinate with the processing unit to balance workloads across operations. To optimize the filtering process, the divisibility test unit can store recent divisor checks and cross-reference those with newly generated candidate numbers to reduce repeated calculations. This configuration of the divisibility test unit supports a high-speed, efficient prime-checking process, contributing to reliable identification of prime numbers for subsequent processing and validation.
In an embodiment, the system comprises a caching unit within the memory unit that stores intermediate results from prior computations to expedite subsequent operations within the prime-checking component. This caching unit retains results from previously executed operations, such as partial divisibility checks, filtered candidate values, and confirmed prime numbers, allowing for rapid retrieval during future calculations. By storing intermediate results, the caching unit reduces the necessity for repetitive calculations, thereby conserving computational time and resources. The caching unit may connect directly with the processing unit, enabling the storage of results immediately after an arithmetic operation, ensuring that frequently accessed data is readily available. The caching unit may organize stored results by ranges of candidate numbers, which supports efficient access according to the specific range needed for ongoing divisibility tests or prime checking. Additionally, the caching unit may employ data prioritization strategies, retaining the most frequently accessed values while periodically refreshing the cache based on frequency of use and system demand. When the prime-checking component requires access to previously evaluated divisibility results, the caching unit allows instant retrieval, bypassing the need for duplicate calculations. The caching unit's structured storage design supports systematic management of memory resources, dynamically adjusting allocation to meet the demands of prime generation.
In an embodiment, the random number generator selects candidate values from a non-linear sequence to optimize the diversity of generated prime numbers. Unlike simple linear sequences, the random number generator may apply mathematical models, such as polynomial functions or pseudorandom number generation techniques, to create a varied set of candidate values. By drawing values from a non-linear sequence, the generator minimizes repetition and predictable patterns, reducing the occurrence of consecutive or similar numbers. This non-linear sequence may be configured according to system parameters, allowing customization in the range and distribution of values based on the target prime ranges. Additionally, the generator may interface with the control unit to dynamically modify sequence parameters, adjusting the non-linear function or distribution pattern based on historical generation data. To avoid duplicating previously evaluated values, the generator may reference historical data stored in memory unit. This approach prevents redundancy, enhancing the diversity of candidate values introduced for prime checking. The non-linear output method is particularly effective for generating large prime numbers, as it enables efficient coverage of wide numeric ranges without bias, expanding the pool of unique candidate values available for further verification.
In an embodiment, the system includes an adaptive threshold adjuster that refines the selection range of candidate values based on historical generation data, with the threshold adjuster dynamically altering the range of the random number generator. This adaptive threshold adjuster evaluates prior data on generated prime numbers, allowing the system to adjust the candidate selection range to emphasize regions more likely to contain primes. The threshold adjuster may apply statistical models or probability distributions to pinpoint numeric intervals where primes are denser. This enables the system to modify the random number generator's output range by expanding or narrowing the interval depending on past results. The threshold adjuster may also adjust its criteria incrementally, learning from cumulative generation patterns and refining selection criteria to support efficient prime selection. The threshold adjuster may retrieve stored data from memory unit, which allows the adjuster to set thresholds based on recent generation results. By narrowing the candidate range to high-probability intervals, the threshold adjuster reduces the computational load by minimizing the number of low-probability candidates sent for divisibility checks.
In an embodiment, the system comprises a parallel processing module within the processing unit that allocates separate processing cores to segments of candidate values, accelerating prime number generation and verification. This parallel processing module divides the candidate set into segments, assigning each segment to a dedicated core for independent analysis. By enabling simultaneous processing, this module reduces the time required to verify large sets of candidates. The architecture of the parallel processing module enables dynamic workload distribution, ensuring that each core receives a balanced workload suitable for the specific processing needs. Each core independently handles divisibility tests or modular operations on its assigned segment, which further streamlines processing. The parallel processing module may adjust workload distribution among cores in real-time based on system performance metrics. Additionally, each core may access the memory unit to retrieve common candidate pools or intermediate results without redundancy. The module's parallel configuration allows each processing unit to achieve high-speed prime checking by avoiding single-thread bottlenecks, which maximizes efficiency for high-volume prime generation tasks.
In an embodiment, the verification component comprises an error detection unit configured to cross-verify prime numbers against a probabilistic criterion to reduce computational load. This error detection unit performs secondary checks on candidate numbers by applying probabilistic tests, such as probabilistic primality tests, to determine prime status with high confidence. By leveraging probabilistic methods, the error detection unit optimizes the verification process by reducing the need for comprehensive divisibility checks, which are more computationally intensive. The error detection unit may retrieve probabilistic verification criteria from the control unit, ensuring that each test aligns with system-defined standards for accuracy. Upon determining a candidate is prime, the unit may conduct further probabilistic tests using random samples or modular congruences to confirm the result's reliability. This method provides an effective balance between accuracy and speed, validating results while minimizing resource-intensive operations. The error detection unit may also adapt its testing criteria, increasing thresholds for additional verification if previous operations report higher error rates.
In an embodiment, the control unit comprises a timing unit that monitors execution times of arithmetic operations within the processing unit, adjusting processing speed based on observed values. This timing unit tracks the duration of each operation, including modular calculations, divisibility tests, and data retrieval tasks, ensuring that they meet pre-established time thresholds. By analyzing these time metrics, the timing unit identifies any operational delays or variations in processing speed, which allows it to dynamically adjust processing parameters to maintain balance across tasks. The timing unit may work in conjunction with the parallel processing module, coordinating workloads across multiple processing cores based on available capacity to sustain efficient execution of operations. The timing unit may also incorporate feedback mechanisms, detecting slower operations and adjusting processing speed accordingly to optimize throughput. Additionally, the timing unit can manage power consumption by controlling processing speed based on the current workload, sustaining performance without overextending resources.
In an embodiment, the system comprises a reporting unit that analyzes prime number distributions generated by the system, with the reporting unit outputting data visualizations to the output unit. The reporting unit gathers verified prime number data, organizing these values into patterns that reveal distribution characteristics across specific numeric ranges. This reporting unit can generate statistical representations that detail the frequency, density, or clustering of primes within set intervals, aiding users in assessing prime distribution properties. The reporting unit may create visualizations, such as histograms, graphs, or frequency charts, to represent the statistical characteristics of generated primes, displaying these results on the output unit. Additionally, the reporting unit may aggregate historical prime generation data to compare current generation patterns with established baselines, offering insight into generation process consistency and potential optimization areas. The reporting unit may apply statistical tools, such as variance analyses or trend analyses, to detect deviations or patterns in prime distribution data, enhancing the understanding of generation trends within the system.
FIG. 2 illustrates a flowchart of the structured method for generating and verifying prime numbers, in accordance with the embodiments of the present disclosure. It begins with the random number generator producing a candidate value within a defined range. This candidate is stored in the memory unit, making it available for subsequent operations. The candidate then undergoes primality assessment by the prime-checking component, which evaluates its divisibility based on specific prime factors. If the candidate is determined to be prime, it proceeds to the verification component, where it is compared against predefined verification criteria. If the candidate meets all verification standards, it is sent to the output unit, where it is recorded as a validated prime number. If the candidate fails the primality check or verification, the process loops back to generate a new candidate, repeating the steps. Throughout this process, the control unit orchestrates each component's interaction, ensuring a smooth and efficient workflow from generation to validation.
In an embodiment, a processing unit performs arithmetic operations associated with prime number generation, providing a foundation for efficient candidate number analysis. The processing unit executes a range of mathematical operations, including modular arithmetic, factorization, and divisibility checks, each essential for generating and verifying prime numbers. By handling these complex calculations, the processing unit reduces the computational load on other system components and accelerates the overall prime generation process. Additionally, the processing unit dynamically manages resource allocation, adjusting workload distribution based on processing demand. This adaptability allows the processing unit to balance speed and accuracy, optimizing the prime-checking process without sacrificing reliability. The processing unit further interacts with other system components, such as the memory unit and prime-checking component, ensuring a seamless data flow that reduces latency and maximizes throughput. By enabling high-speed, resource-efficient prime calculations, the processing unit supports robust performance across varying computational demands.
In an embodiment, a memory unit operatively connected to the processing unit stores candidate values and previously computed prime numbers, enhancing data accessibility and reducing redundant computations. The memory unit retains both raw candidate numbers and processed prime values, allowing quick retrieval during prime-checking and verification. By caching intermediate results, the memory unit minimizes repetitive calculations, effectively lowering computational costs associated with prime generation. The memory unit is structured to provide systematic storage and retrieval, optimizing access times based on processing requirements. Through interaction with the processing unit, the memory unit ensures that stored values are readily available for arithmetic operations and divisibility tests. Additionally, the memory unit supports data caching strategies that enable efficient memory management, retaining high-priority data based on access frequency. This organized data storage accelerates the retrieval process, allowing for rapid reuse of previously computed results and contributing to the overall efficiency of the prime generation system.
In an embodiment, a prime-checking component assesses the primality of candidate values by evaluating divisibility using a predefined set of prime factors. The prime-checking component performs divisibility tests that filter out non-prime candidates early in the process, improving computational efficiency. By applying divisibility checks agains












I/We Claims


A system for generating and verifying prime numbers, comprising:
a processing unit configured to perform arithmetic operations associated with prime number generation;
a memory unit operatively connected to said processing unit and configured to store candidate values and previously computed prime numbers;
a prime-checking component connected to said processing unit, said prime-checking component configured to assess the primality of candidate values by evaluating divisibility based on a set of prime factors;
a random number generator connected to said processing unit, said random number generator configured to produce candidate values within a defined range;
a verification component configured to compare computed prime numbers against a predefined verification criterion;
an output unit configured to output a list of validated prime numbers upon verification of primality by said verification component;
a control unit configured to manage interactions between said processing unit, prime-checking component, random number generator, verification component, and output unit to facilitate the generation and verification of prime numbers.
The system of claim 1, wherein said prime-checking component comprises a divisibility test unit configured to filter non-prime numbers based on the properties of modular arithmetic.
The system of claim 1, further comprising a caching unit within said memory unit configured to store intermediate results from prior computations, such that retrieval of previously computed results expedites subsequent operations within said prime-checking component.
The system of claim 1, wherein said random number generator is configured to select candidate values from a non-linear sequence to optimize the diversity of generated prime numbers.
The system of claim 1, further comprising an adaptive threshold adjuster configured to refine the selection range of candidate values based on historical generation data, wherein said threshold adjuster dynamically alters the range of said random number generator.
The system of claim 1, further comprising a parallel processing module within said processing unit configured to allocate separate processing cores to segments of said candidate values, such that prime number generation and verification are accelerated.
The system of claim 1, wherein said verification component comprises an error detection unit configured to cross-verify prime numbers against a probabilistic criterion to reduce computational load.
The system of claim 1, wherein said control unit comprises a timing unit configured to monitor execution times of arithmetic operations within said processing unit and to adjust processing speed based on observed values.
The system of claim 1, further comprising a reporting unit configured to analyze prime number distributions generated by said system, wherein such reporting unit outputs data visualizations to said output unit.
A method for generating and verifying prime numbers, comprising the steps of:
generating a candidate value within a defined range by means of a random number generator;
storing said candidate value in a memory unit for subsequent retrieval and processing;
assessing primality of said candidate value by a prime-checking component by applying a divisibility test using a defined set of prime factors;
comparing said candidate value with verification criteria within a verification component, wherein said verification component validates primality if said candidate value meets said verification criteria;
outputting validated prime numbers to an output unit for use in further computations or display;
managing the interactions of said random number generator, prime-checking component, memory unit, verification component, and output unit by a control unit to facilitate efficient generation and verification of prime numbers.




Disclosed is a system for generating and verifying prime numbers, comprising a processing unit performing arithmetic operations to generate prime numbers. A memory unit stores candidate values and previously computed prime numbers. A prime-checking component assesses primality by evaluating divisibility using a predefined set of prime factors. A random number generator produces candidate values within a defined range, and a verification component compares computed prime numbers against a predefined verification criterion. An output unit provides a list of validated prime numbers upon successful verification. A control unit manages interactions among the processing unit, prime-checking component, random number generator, verification component, and output unit to enable prime number generation and verification.

, Claims:I/We Claims


A system for generating and verifying prime numbers, comprising:
a processing unit configured to perform arithmetic operations associated with prime number generation;
a memory unit operatively connected to said processing unit and configured to store candidate values and previously computed prime numbers;
a prime-checking component connected to said processing unit, said prime-checking component configured to assess the primality of candidate values by evaluating divisibility based on a set of prime factors;
a random number generator connected to said processing unit, said random number generator configured to produce candidate values within a defined range;
a verification component configured to compare computed prime numbers against a predefined verification criterion;
an output unit configured to output a list of validated prime numbers upon verification of primality by said verification component;
a control unit configured to manage interactions between said processing unit, prime-checking component, random number generator, verification component, and output unit to facilitate the generation and verification of prime numbers.
The system of claim 1, wherein said prime-checking component comprises a divisibility test unit configured to filter non-prime numbers based on the properties of modular arithmetic.
The system of claim 1, further comprising a caching unit within said memory unit configured to store intermediate results from prior computations, such that retrieval of previously computed results expedites subsequent operations within said prime-checking component.
The system of claim 1, wherein said random number generator is configured to select candidate values from a non-linear sequence to optimize the diversity of generated prime numbers.
The system of claim 1, further comprising an adaptive threshold adjuster configured to refine the selection range of candidate values based on historical generation data, wherein said threshold adjuster dynamically alters the range of said random number generator.
The system of claim 1, further comprising a parallel processing module within said processing unit configured to allocate separate processing cores to segments of said candidate values, such that prime number generation and verification are accelerated.
The system of claim 1, wherein said verification component comprises an error detection unit configured to cross-verify prime numbers against a probabilistic criterion to reduce computational load.
The system of claim 1, wherein said control unit comprises a timing unit configured to monitor execution times of arithmetic operations within said processing unit and to adjust processing speed based on observed values.
The system of claim 1, further comprising a reporting unit configured to analyze prime number distributions generated by said system, wherein such reporting unit outputs data visualizations to said output unit.
A method for generating and verifying prime numbers, comprising the steps of:
generating a candidate value within a defined range by means of a random number generator;
storing said candidate value in a memory unit for subsequent retrieval and processing;
assessing primality of said candidate value by a prime-checking component by applying a divisibility test using a defined set of prime factors;
comparing said candidate value with verification criteria within a verification component, wherein said verification component validates primality if said candidate value meets said verification criteria;
outputting validated prime numbers to an output unit for use in further computations or display;
managing the interactions of said random number generator, prime-checking component, memory unit, verification component, and output unit by a control unit to facilitate efficient generation and verification of prime numbers.

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