Browse Definitions:
Definition

prime number

A prime number is a whole number greater than 1, whose only two whole-number factors are 1 and itself.  The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.  

As we proceed in the set of natural numbers N = {1, 2, 3, ...}, the primes become less and less frequent in general.  However, there is no largest prime number.  For every prime number p, there exists a prime number p' such that p' is greater than p.  This was demonstrated in ancient times by the Greek mathematician Euclid.

Suppose n is a whole number, and we want to test it to see if it is prime.   First, we take the square root (or the 1/2 power) of n; then we round this number up to the next highest whole number.  Call the result m.  We must find all of the following quotients:

qm = n / m
q(m-1) = n / (m-1)
q(m-2) = n / (m-2)
q(m-3) = n / (m-3)
. . .
q3 = n / 3
q2 = n / 2

The number n is prime if and only if none of the q's, as derived above, are whole numbers.

A computer can be used to test extremely large numbers to see if they are prime.  But, because there is no limit to how large a natural number can be, there is always a point where testing in this manner becomes too great a task even for the most powerful supercomputers.  Various algorithms have been formulated in an attempt to generate ever-larger prime numbers.  These schemes all have limitations.

A Mersenne prime must be reducible to the form 2 n - 1, where n is a prime number. The first few known values of n that produce Mersenne primes are where n = 2, n = 3, n = 5, n = 7, n = 13, n = 17, n = 19, n = 31, n = 61, and n = 89.

A Fermat prime is a Fermat number that is also a prime number . A Fermat number n is of the form 2 m + 1, where m is the n th power of 2 (that is, m = 2 n , where n is an integer). 

This was last updated in June 2015

Continue Reading About prime number

Start the conversation

Send me notifications when other members comment.

By submitting you agree to receive email from TechTarget and its partners. If you reside outside of the United States, you consent to having your personal data transferred to and processed in the United States. Privacy

Please create a username to comment.

-ADS BY GOOGLE

File Extensions and File Formats

Powered by:

SearchCompliance

  • pure risk (absolute risk)

    Pure risk, also called absolute risk, is a category of threat that is beyond human control and has only one possible outcome if ...

  • risk assessment

    Risk assessment is the identification of hazards that could negatively impact an organization's ability to conduct business.

  • audit program (audit plan)

    An audit program, also called an audit plan, is an action plan that documents what procedures an auditor will follow to validate ...

SearchSecurity

SearchHealthIT

SearchDisasterRecovery

  • business continuity and disaster recovery (BCDR)

    Business continuity and disaster recovery (BCDR) are closely related practices that describe an organization's preparation for ...

  • business continuity plan (BCP)

    A business continuity plan (BCP) is a document that consists of the critical information an organization needs to continue ...

  • call tree

    A call tree -- sometimes referred to as a phone tree -- is a telecommunications chain for notifying specific individuals of an ...

SearchStorage

  • nearline storage

    Nearline storage is the on-site storage of data on removable media.

  • application-aware storage

    Application-aware storage is a storage system with built-in intelligence about relevant applications and their utilization ...

  • Remote Direct Memory Access (RDMA)

    Remote Direct Memory Access (RDMA) is a technology that allows computers in a network to exchange data in main memory without ...

SearchSolidStateStorage

  • 3D XPoint

    3D XPoint is memory storage technology jointly developed by Intel and Micron Technology Inc.

  • RRAM or ReRAM (resistive RAM)

    RRAM or ReRAM (resistive random access memory) is a form of nonvolatile storage that operates by changing the resistance of a ...

  • JEDEC

    JEDEC is a global industry group that develops open standards for microelectronics.

SearchCloudStorage

  • Google Cloud Storage

    Google Cloud Storage is an enterprise public cloud storage platform that can house large unstructured data sets.

  • RESTful API

    A RESTful application program interface breaks down a transaction to create a series of small modules, each of which addresses an...

  • cloud storage infrastructure

    Cloud storage infrastructure is the hardware and software framework that supports the computing requirements of a private or ...

Close