The first primes are listed below, followed by lists of notable types of prime numbers in alphabetical order, giving their respective first terms. The following table lists the first primes, with 20 columns of consecutive primes in each of the 50 rows. There are known formulae to evaluate the prime-counting function the number of primes below a given value faster than computing the primes.

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Below are listed the first prime numbers of many named forms and types. More details are in the article for the name. Primes that are the number of partitions of a set with n members. The next term has 6, digits. A circular prime number is a number that remains prime on any cyclic rotation of its digits in base Some sources only list the smallest prime in each cycle, for example, listing 13, but omitting 31 OEIS really calls this sequence circular primes, but not the above sequence :. Primes that remain prime when read upside down or mirrored in a seven-segment display.

Primes that become a different prime when their decimal digits are reversed.

## Prime Number

The name "emirp" is obtained by reversing the word "prime". Of the form n!

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Fortunate numbers that are prime it has been conjectured they all are. Primes that are a cototient more often than any integer below it except 1. Odd primes p that divide the class number of the p -th cyclotomic field. They are also called full reptend primes.

## Prime numbers

Primes p for base As of [update] , there are 51 known Mersenne primes. The 13th, 14th, and 51st have respectively , , and 24,, digits. As of [update] , this class of prime numbers also contains the largest known prime: M , the 51st known Mersenne prime.

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As of June , these are the only known double Mersenne primes, and number theorists think these are probably the only double Mersenne primes. For other small a , they are given below:. This form is prime for all positive integers n. Primes for which there is no shorter sub-sequence of the decimal digits that form a prime. There are exactly 26 minimal primes:. Primes p for which the least positive primitive root is not a primitive root of p 2. Three such primes are known; it is not known whether there are more. It seems likely that all further permutable primes are repunits , i.

These are also class 1- primes. Primes for which there are more prime permutations of some or all the decimal digits than for any smaller number. Primes p that do not divide the class number of the p -th cyclotomic field. Also called primes congruent to d modulo a. The fourth Smarandache-Wellin prime is the digit concatenation of the first primes that end with As of [update] , these are the only known Stern primes, and possibly the only existing. Primes that are also a prime number when rotated upside down.

This, as with its alphabetic counterpart the ambigram , is dependent upon the typeface. Primes that are both left-truncatable and right-truncatable. There are exactly fifteen two-sided primes:. As of [update] , no Wall-Sun-Sun primes are known. Primes that having any one of their base 10 digits changed to any other value will always result in a composite number. Numbers that are not prime numbers are called composite numbers. You may have noticed that every even number greater than 2 is a composite number.

This is because every even number greater than 2 is divisible by 2, so they cannot be primes. Thus, 2 is the only even prime number! Here is a list of the 25 prime numbers between 1 and Although some experts believe that the ancient Egyptians knew about prime numbers, it was the ancient Greeks who first studied prime numbers in depth. In fact, it was Greek mathematician Euclid who proved that an infinite number of prime numbers exists.

So that list of prime numbers above just keeps going and going …. According to the fundamental theorem of arithmetic , every positive whole number greater than 1 can be written as a unique product of one or more prime numbers. If you're wondering about the largest prime number found to date, it's pretty big! In , a group of people used the combined computing power of hundreds of computers to discover a prime number that has approximately 13 million digits!

Grab 2, 3, 5, or even 7 friends and family members to help you explore one or more of the following prime activities! I don't understand how 2 is prime.

Plus the article was super helpful! Hi, Odom! Two actually has only 2 natural number divisors - 1 and 2. Zero is not included. We hope that helps!

## Prime Number Calculator

Great explanation, Collin! A prime number is any number not divisible evenly by any number except itself. You gave great examples! Great to hear, Marin! We love when we're learning and having fun, all at the same time! We're glad it was helpful! I think this is very helpful for learning cool and exiting ways to know what prime numbers are to learn about them. Great to hear, Jeff!

We appreciate the feedback. We love when we are learning and having fun, all at the same time! Excellent post. I was checking continuously this blog and I am impressed! Extremely useful information specially the last part : I care for such info a lot. I was looking for this certain info for a long time. Thank you and good luck. Welcome May! I guessed it on the day when the wonder of the day was about minecraft. I remember when we were learning prime and composite numbers they were fun and easy, and I just wanted to say to all the little kids I think you may have a good time learning them too!!!

It's so neat to see so many diferent ways of thinking about numbers. I think prime numbers is defenftly my favorite subject. Not to worry, RodMan, sometimes it takes some time to grasp the idea of prime numbers. We Wonder if you can take a look at the Wonder again and help us understand where you're confused.

I know that a prime number has two factors one and itself and composite number has more than two factors. I learned this in math class! Thanks for sharing your background knowledge about prime numbers, Julie! You are a super smart Wonder Friend! We're glad to have you as a new friend! Hi wonderopolis! I like how you brought math into your website.

I like it when two subjects combined! Hey, Wonder Friends! Before you submit your comment, please remember:. Comments are subject to approval and may not be published if they are not appropriate for the Wonder discussion. Drag a word to its definition. You have answered 0 of 3 questions correctly and your score is:.

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Want to add a little wonder to your website? Help spread the wonder of families learning together. We sent you SMS, for complete subscription please reply. Follow Twitter Instagram Facebook. What is a prime number? How many prime numbers are there? What is the largest known prime number? Tags: See All Tags algorithm , cipher , composite , cryptography , divide , division , Egyptian , encrypting , encryption , Eratosthenes , Euclid , factor , fundamental , Greek , infinite , infinity , Math , mathematical , mathematician , mathematics , number , numerical , prime , prime numbers , sieve , theorem , trivia.

Wonder What's Next? Better hold your nose. Try It Out Grab 2, 3, 5, or even 7 friends and family members to help you explore one or more of the following prime activities! Ready to Be a Prime Number Hunter? Just print out a Chart , grab some markers, and get ready to do some fancy cipherin'! As you hunt, circle the prime numbers and cross out the composite numbers.

You'll probably begin to see some shortcuts that you can take. For example, you know that 2 is the only even prime number, so you can cross out all the other even numbers. You also know that 3 is a prime number, so you can cross out all the multiples of 3: 6, 9, 12, 15 and so on. As you do this with each prime number you find, you'll quickly narrow down the list of numbers to just the primes. The shortcut you discovered in the first activity above was actually discovered by ancient Greek mathematician Eratosthenes.

He developed a simple algorithm for finding all the prime numbers up to a specific whole number. His famous algorithm is called the Sieve of Eratosthenes.

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If you want, you can check out an interactive version of the Sieve of Eratosthenes online! Up for a challenge? Jump online to check out Math Forum: Prime Numbers. You'll go beyond simple prime number definition to learn about both Euclid's theory of prime numbers which has been proven and Goldbach's Conjecture which hasn't.

Did you get it? Test your knowledge. Wonder Words number prime factor positive digit divisible multiply composite infinite fundamental arithmetic mathematician theorem unique Take the Wonder Word Challenge. Join the Discussion. Wonderopolis Jun 4, Thanks for the additional information! Wonderopolis Dec 19, We're so glad to hear that, braylon!