Browse Definitions :
Definition

prime number

A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole numbers that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. Numbers that have more than two factors are called composite numbers. The number 1 is neither prime nor composite. 

prime number chart

For every prime number p, there exists a prime number p' such that p' is greater than p.  This mathematical proof, which was demonstrated in ancient times by the Greek mathematician Euclid, validates the concept that there is no "largest" prime number. As the set of natural numbers N = {1, 2, 3, ...} proceeds, however, prime numbers generally become less frequent and are more difficult to find in a reasonable amount of time. As of this writing, the largest known prime number has more than 23 million digits. It is referred to as M77232917 and has one million more digits than the previous record holder. 

How to determine if a number is prime

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. For example, suppose n is a whole number, and it is not yet known if n is prime or composite. First, take the square root (or the 1/2 power) of n; then round this number up to the next highest whole number and call the result m.  Then 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.

Mersenne and Fermat primes

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.

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). 

Prime numbers and cryptopgraphy

Encryption always follows a fundamental rule: the algorithm (the actual procedure being used) doesn't need to be kept secret, but the key does. Even the most sophisticated hacker in the world will be unable to decrypt data as long as the key remains secret -- and prime numbers are very useful for creating keys. For example, the strength of public/private key encryption lies in the fact that it's easy to calculate the product of two randomly chosen prime numbers, but it can be very difficult and time consuming to determine which two prime numbers were used to create an exteremely large product, when only the product is known.

In RSA (Rivest-Shamir-Adleman) public key cryptography, prime numbers are always supposed to be unique. The primes used by the Diffie-Hellman key exchange and the Digital Signature Standard (DSA) cryptography schemes, however, are frequently standardized and used by a large number of applications.

This was last updated in January 2018

Continue Reading About prime number

Join the conversation

12 comments

Send me notifications when other members comment.

Please create a username to comment.

what are some prime numbers from 2 to 100 and i did not understand but thanks for trying.
Cancel
According to the first algorithm, if n = 2, then
sqrt(n) = 1.4142...
m = 2
q(m) = n/m = 1 => q is a whole number, but 2 is a prime number.

You need to add one more condition that q == 1 is not considered in "none of the q's, as derived above, are whole numbers"
Cancel
Zero is a prime number or not?
Cancel
no cause you can get zero with any number multiplied by zero 
0 = 0 x N
Cancel
it is not a prime number
Cancel
Thanks, you helped me with my homework. This is a helpful website to do all homework. Thanks again.
Cancel
Thanks for this helped a lot.
Cancel

bga126 thats my c**e i don't understand literally everything but thx for trying
Cancel
Same at least they tried lol.
Cancel
What I don't get it?
Cancel
Hi im mom and i love math 
Cancel
What are some tricks for square roots?

Cancel

-ADS BY GOOGLE

File Extensions and File Formats

Powered by:

SearchCompliance

  • California Consumer Privacy Act (CCPA)

    The California Consumer Privacy Act (CCPA) is legislation in the state of California that supports an individual's right to ...

  • compliance audit

    A compliance audit is a comprehensive review of an organization's adherence to regulatory guidelines.

  • regulatory compliance

    Regulatory compliance is an organization's adherence to laws, regulations, guidelines and specifications relevant to its business...

SearchSecurity

  • endpoint detection and response (EDR)

    Endpoint detection and response (EDR) is a category of tools and technology used for protecting computer hardware devices–called ...

  • ransomware

    Ransomware is a subset of malware in which the data on a victim's computer is locked, typically by encryption, and payment is ...

  • single sign-on (SSO)

    Single sign-on (SSO) is a session and user authentication service that permits an end user to enter one set of login credentials ...

SearchHealthIT

SearchDisasterRecovery

  • disaster recovery team

    A disaster recovery team is a group of individuals focused on planning, implementing, maintaining, auditing and testing an ...

  • cloud insurance

    Cloud insurance is any type of financial or data protection obtained by a cloud service provider. 

  • business continuity software

    Business continuity software is an application or suite designed to make business continuity planning/business continuity ...

SearchStorage

  • blockchain storage

    Blockchain storage is a way of saving data in a decentralized network which utilizes the unused hard disk space of users across ...

  • disk mirroring (RAID 1)

    RAID 1 is one of the most common RAID levels and the most reliable. Data is written to two places simultaneously, so if one disk ...

  • RAID controller

    A RAID controller is a hardware device or software program used to manage hard disk drives (HDDs) or solid-state drives (SSDs) in...

Close