What makes 13

For instance, if we point out 31 as a prime number outside the list of first 10 primes mentioned before, we will indeed show that that list did not include all prime numbers. But perhaps by adding 31 we have now found all of the prime numbers, and there are no more? What we need to do, and what Euclid did 2, years ago, is to present a convincing argument why, for any finite list, as long as it may be, we can find a prime number that is not included in it.

If you pick a number that is not composite, then that number is prime itself. Otherwise, you can write the number you chose as a product of two smaller numbers. If each of the smaller numbers is prime, you have expressed your number as a product of prime numbers.

If not, write the smaller composite numbers as products of still smaller numbers, and so forth. In this process, you keep replacing any of the composite numbers with products of smaller numbers. Since it is impossible to do this forever, this process must end and all the smaller numbers you end up with can no longer be broken down, meaning they are prime numbers. As an example, let us break down the number 72 into its prime factors:.

We will demonstrate the idea using the list of the first 10 primes but notice that this same idea works for any finite list of prime numbers. Let us multiply all the numbers in the list and add one to the result. Let us give the name N to the number we get.

The value of N does not actually matter since the argument should be valid for any list. The number N , just like any other natural number, can be written as a product of prime numbers. Who are these primes, the prime factors of N?

We do not know, because we have not calculated them, but there is one thing we know for sure: they all divide N. But the number N leaves a remainder of one when divided by any of the prime numbers on our list 2, 3, 5, 7,…, 23, This is supposed to be a complete list of our primes, but none of them divides N.

So, the prime factors of N are not on that list and, in particular, there must be new prime numbers beyond Have you found all the prime numbers smaller than ? Which method did you use? Did you check each number individually, to see if it is divisible by smaller numbers? If this is the way you chose, you definitely invested a lot of time. Eratosthenes Figure 1 , one of the greatest scholars of the Hellenistic period, lived a few decades after Euclid.

He served as the chief librarian in the library of Alexandria , the first library in history and the biggest in the ancient world. Among other things, he designed a clever way to find all the prime numbers up to a given number. Since this method is based on the idea of sieving sifting the composite numbers, it is called the Sieve of Eratosthenes.

We will demonstrate the sieve of Eratosthenes on the list of prime numbers smaller than , which is hopefully still in front of you Figure 2. Circle the number 2, since it is the first prime number, and then erase all its higher multiples, namely all the composite even numbers. Move on to the next non-erased number, the number 3.

Since it was not erased, it is not a product of smaller numbers, and we can circle it knowing that it is prime. Again, erase all its higher multiples. Notice that some of them, such as 6, have been already deleted, while others, such as 9, will be erased now. The next non-erased number—5—will be circled. Again, erase all its higher multiples: 10, 15, and 20 have already been deleted, but 25 and 35, for instance, should be erased now.

Continue in the same manner. Until when? All numbers smaller than that were not erased are prime numbers and can be safely circled!

What is the frequency of prime numbers? How many prime numbers are there, approximately, between 1,, and 1,, one million and one million plus one thousand and how many between 1,,, and 1,,, one billion and one billion plus one thousand?

Can we estimate the number of prime numbers between one trillion 1,,,, and one trillion plus one thousand? Calculations reveal that prime numbers become more and more rare as numbers get larger. But is it possible to state an accurate theorem that will express exactly how rare they are? Such a theorem was first stated as a conjecture by the great mathematician Carl Friedrich Gauss in , at the age of Sep 21, Sacha Sep 11, I don't think 13 a bad number it actually it one of my favorite numbers.

Sep 14, Samantha Dec 3, I don't believe in superstitions but they are fun to hear! Wonderopolis Dec 4, I was born on June 13th, so I do not think it is bad luck, but I do think Friday the 13th is unlucky and my birthday this year is on Friday the 13th, so wish me luck.

Wonderopolis Apr 14, And, Happy Birthday on June 13th! We think it will be a lucky day! Team Clark 25 Dec 13, I just learned that the fear of the number 13 is called triskiadekaphobia. I've heard that crossing your fingers and the number 7 is good luck, and I've heard that breaking a mirror is bad luck. I've never knew what superstition was until now. So thanks for all the things you taught me today Wonderopolis.

Wonderopolis Dec 14, Team Clark Dec 13, Hi Wonderopolis! We enjoyed your wonder about the phobia of the number We didn't know there were so many reasons why people classify the number 13 as unlucky! Could you tell us, are there other examples of phobias for different numbers? If so what are they? We also learned that 7 is a lucky number and the difference between superstitions and phobias.

Thanks for the wonder! Team Clark. Ella Oct 16, Hi Wonderopolis, sorry I'm late in this comment. I loved this wonder. Some people have a hospital-phobia, I think it's called Nosocomephobia.

And some have a fear of their photograph being taken! I think that's called Ipovlopsychophobia, but I don't know. Wonderopolis Oct 16, Thanks Gigi! We're glad you enjoyed this Wonder today! Anna Oct 15, My best friend my all time best friend Brooke was born on the Friday the 13th that's what makes her cool and my bestie.

Stemmet's 3rd grade class Sep 15, Dear Wonderopolis, Why do so many people believe in superstitions? I don't believe in any superstitions, other than if you cross your fingers it brings good luck. What superstitions do you believe in? Why do only certain religions believe in certain superstitions?

Also I learned what knock on wood means. I also learned on airplanes they skip the 13th aisle. Another thing I learned is that people try to skip the 13th street. Some other things I learned is that if a black cat walks by it's bad luck. I learned that if you walk under a ladder it's bad luck. I hope I don't get any bad luck today. Wonderopolis Sep 16, From Andrew L: I wonder if superstitions are real.

Wonderopolis Sep 13, Elisa Mar 24, I love the number It is my favorite number and, by coincidence, my lucky number. My birthday is the 31st day of March Easter and all my friends and I flip our birthday number around to make it our lucky numbers, so mine is Wonderopolis Mar 25, ACT Mar 21, My brother's birthday is on the 13th and his 13th birthday it was Friday the 13th.

Wonderopolis Mar 21, Niki Jan 20, Wonderopolis Jan 20, Dear Wonderopolis, WOW! That article about the number 13 being unlucky was really cool! One new thing that I learned was that if the mere mention of 13 makes you uneasy of nervous you may suffer of triskaidekaphobia. How do you get triskaidekaphobia? How long do you usally have the phobia? Another thing that I learned was that it is the square root of ! Do people abhor triskaidekaphobia? I cannot wait to see what the new wonder will be!

Your reader, Emma. Wonderopolis Dec 13, Hi Wonderopolis, Thanks for letting me know I have both triskaidekaphobia and paraskevidekatriaphobia. Thanks for letting my know those both colossal words. Are there other numbers unlucky like the number 13?? If so please list them. It will be really cool if you could list a lot of superstitions for me to know. Once again thank you very much for posting this wonder Thanks, Shevani S.

Wonderopolis Dec 12, Nov 29, For some weird reason I don't really like odd numbers. I like even ones better. So I've never really liked 1,3,5,7,9,11, Except I do like 1 so I don't like any odd numbers except for one. Wonderopolis Nov 30, Tyler Jarvis Nov 28, All of this Friday the 13 stuff is a bunch of nonsense. OK so those events happened on the 13th. Those were a coincidence. Wonderopolis Nov 28, Skye Oct 12, My favorite number is , but I think 13 is lucky.

Wonderopolis Oct 13, Black cats were considered lucky in Egyptian culture. Wonderopolis Apr 26, Hey I've got some made-up phobia's!! Wonderopolis Apr 17, Team Mc. Neil 11 Apr 13, Hi, I just learned that arachibutyrophobia is the fear of peanut butter sticking to the roof of your mouth!!

I also learned that lutraphobia is the fear of otters. Two new vocabulary words I learned are coulrophoia the fear of clowns and aulophobia the fear of flutes. The one thing that I really can't believe is that there is a fear of getting tickled by badgers while jumping rope!!! That is so specific!!! I still have one more question, is there a fear of food!!! Wonderopolis Apr 13, TeamMcneil17 Apr 12, I never knew that triskaidekaphobia meant that you were afraid of the number I also never knew that Coulrophobia meant that you were afraid of clowns.

I'm just curious but what is the most common know "phobia"? Also, what is the "phobia" most people are scared of? Team McNeil 10 Apr 5, Hi, Wonderopolis I learned a lot of things from the article. I learned two new words 1: triskaidekaphobia 2: superstition. I also learned that in building they skip the 13th floor and, that on streets they skip the 13th street. Is there any other unlucky numbers? Are factors of 13 unlucky too? Do you have an unlucky number? Thank you for listening Wonderopolis.

Wonderopolis Apr 5, I got it wrong the number was 8. Wonderopolis Apr 4, Team McNeil Apr 2, This wonder really helped me understand about reasons why 13 is unlucky!

I think I may have triskadekaphobia because I always feel a bit shaky when the number 13 is mentioned. How do we know when this superstition was created? Do we have documents about this topic? Although I have many questions I have learned a lot.

For example now I know the name of the fear of Friday the 13th paraskevidekatriaphobia which I totally have. Who knew there was a fear of otters lutraphobia!!!!!!!!

Thank you for having this website!!!!!!!!!!!! Wonderopolis Apr 3, Team Unger 14 Apr 1, Who knew there was a fear of the number 13? I think triskadekaphobia is weird. I had no idea that there was such thing as fear of Friday the 13 or paraskevidekatriaphobia. I didn't know fear of the number 13 was more common in western cultures.

Do you know how many people have triskadekaphobia? Wonderopolis Apr 1, Team Clark 16 Mar 29, Hey wonderopolis!!!! It is so cool that our class found this wonder because we are studying the suffix phobe and phobia. It is cool that there is a name for being superstitious or being feared of the number The word is triskaiphobia. I wonder if some cities on Friday the 13th are in total pandemonium?

Are you scared of the number 13? Wonderopolis Mar 30, Team Wilch 14 Mar 29, Hola Wonderopolis, WOW! Why do the people who name phobias make them so long and confusing!?! I believe that phobias are fun but not at all real.

At times, believing in phobias can be a really big conundrum because people try to avoid things and it can lead to problems. Does believing too many phobias ever lead to depression because they are scared of so much? I learned that there is a lot of fears and names for practically all of them! Who would be afraid of being tickled by badgers while jumping rope? Why is the fear of the number 13 only common in the west? I also learned why people think that 13 is an unlucky number.

I have to go now, Bye! Wonderopolis Mar 29, Team clark 14 Mar 29, I Wonder why people are afraid of things. I know some. Hi I think being triskaidecaphobic is kinda dumb no offence to those who are triskaidecaphobes. I also think that the fear of 13 should be a superstition. I do not believe in anything supernatural like aliens and ghosts but I do think that knocking on wood twice brings good luck.

I am completely afraid of spiders. Whenever I see a spider, it's a complete pandamoneom! Thanks for giving me a good wonder! Wilch 1 Mar 29, Hello Wonderopolis, I learned that Arachibutyrophobia is the fear of peanut butter sticking to the roof of the mouth. I agree that triskaidekaphobia is a superstition and not a phobia.

I also learned that phobias can cause you a conundrum. I wonder how many phobias there are. Hello Wonderopolis, I thought it was very interesting reading about Triskaidekaphobia and other phobias. I still don't see the pandemonium is about thirteen. I like the number thirteen a lot. I only really have one fear and it is centipedes and millipedes a lot, but I am fine with spiders and clowns. What is the fear of centipedes do you know?

While I was reading, I saw that there was a fear of being tackled by a badger while jumping rope, that just scares me that that's a phobia! I learned many new phobias. In triskaidekaphobia, there are many things people are scared about. I learned how some people have a fear of losing their cell phone contacts.

There is also a fear of otters some people have. How many fears do people have for Friday the 13th? I never knew how Friday the 13th is such a conundrum for people. I really enjoyed reading about Friday the 13th fears. Thank you!! Team Wilch16 Mar 29, One was coulrophobia phobia of clowns. Another one that I leaned was arachibutyrophobia-peanut butter sticking to the roof of the mouth. I thought that was funny. I wonder why 13 such a unlucky number, because there's a 13 in my class and he says it's his lucky number.

I am not trying to be persnickity, but do you have any phobias? I really enjoyed the article. Thank you! Team Wilch 11 Mar 29, Hey Wonderopolis! I was very interested about all of the phobias that there are. It strikes me as funny some of the things people are scared of.

Peanut butter sticking to the roof of your mouth? NO gravity, being tickled by badgers while jumping rope? I want to know about what the most common superstition is? I also discovered that I am afraid of spiders, but don't know what it's called. The conundrum of how 13 got unlucky will never be truly known.

Team Wilch 9 Mar 29, I think that this wonder is so cool! I'm not fearful of the number 13, but I am a little superstitious. I'm afraid of spiders what is that called? I think Friday the 13th on the year will be pandemonium.

Some phobias are really silly like the one of peanut butter sticking to the top of your mouth. Team Wilch 9. I enjoyed learning about phobias. I didn't know that most hotels and tall buildings skip the 13th floor. I think triskaidekaphobia is considered a phobia. What do you think whether triskaidekaphobia is considered as a phobia or a superstition? I think it will be conundrum if everyone had bad day on 13th!

Thanks for making me wonder! Team Wilch Team Wilch10 Mar 29, Dear wonderopolis, Some phobias are very interesting. I have Coulrophobia. I am very scared of clowns. I think that clowns are very scary. I can't believe that some people have fears of peanut butter sticking to the roof of your mouth, and people are scared of flutes!

Also being tickled by badgers while jumping rope! That's strange. Do you have any strange phobias like those ones?

I wonder why Friday the 13th is such a Pandemonium. Also I wonder what it will be like when its Friday the 13th in ! Team Wilch Team Wilch13 Mar 29, Hello Wonderopolis, I enjoyed reading about triskaidekaphobia. The weird thing is, 13 is my luckiest number. I have that number in football and basketball. I am kind've superstitious because I always get freaked out on tests, when two answers in a row are the same letter.

I'm not that superstitious though because I don't believe that if a black cat walks by you, you will have bad luck. I can't believe that it went all the way back to Jesus, that is such a long time ago. I wonder why Friday the 13th is such a pandemonium. I wonder what some other unlucky numbers there are, is 23 unlucky? Thanks for making me Wonder.

Team Wilch 2 Mar 29, I don't have triskaidekaphobia. I actually like the number I think it is cool to learn about the fear of the number 13 as a phobia.

I just wondered how many phobias are there? What is the most common phobia? What is the weirdest phobia? Oh I forgot, I wanted to tell you that one time I said the number 13 and a friend of mine had pandemonium which is a wild up roar.

Bye :. Team Wilch 19 Mar 29, Maybe some people think that Friday the 13th is bad luck because maybe something bad happened to them that day. I can't believe that some of the phobias are: Aulophobia Flutes Lutraphobia Otters Nomophobia Losing Cell Phone Contacts Fear of being tickled by badgers while jumping rope Fear of finding a portal to an alternative universe at the back of your closet Fear of your dog actually eating your homework Fear of being followed by lost penguins and Fear of waking up on the ceiling because gravity went away during the night.

Maybe the reason people are afraid of those things is because something might have happened to them when there were little that made them scared of those things.

If the Friday the 13th superstition was real, it would be pandemonium! Team Wilch3 Mar 29, Hi Wonderopolis I think that the passage about the 13 is really cool. I never had a fright of the number 13 unless something happens on the 13th. I like researching this kind of stuff because some people have their own conundrums on the 13th. Some people have triskaidekaphobia which means they are afraid of clowns and some people have Nomophobia.

Not to be persnickety but do you have a fright of the number 13?. Team Wilch3. Team Wilch 12 Mar 29, Hello Wonderopolis I don't know if I have a phobia, but the names of some are really cool! There's so many phobias that somebody could probably make a dictionary of phobias. I think that having a phobia could be a real conundrum.

I think that it could really effect you life forever. Are you born with a phobia? I think that I do not have triskaidekaphobia. In fact, Friday the thirteenth really doesn't scare me at all.

Team Wilch18 Mar 29, I am pretty scared about triskaidekaphobia, because one time in Florida, I took a trolly around town and we stopped and got something to eat and after we ate I forgot my phone, Ipod, and wallet. After we got the things back, we missed the trolly. It was also on Friday the 13th. It will be a phobia I will always be afraid of. I have learned that planes skip the 13th row and that some cities avoid having a 13th street!

I have conundrum question to ask. Whats the most common phobia? Me and my friend think that its not unlucky because it's actually our lucky number along with Hi, Team Wilch 21! Thanks for sharing how you and your friend feel about the number 13! Team Clark12 Mar 29, Hello Wonderopils I kind of have a triskaidekaphobia.

I also have the phobia of Nomophobia, which means losing cell phone contact. Do you have any phobias. I can't believe that it went back to the Jesus and the Vikings. Here's a conundrum Team Clark Team Clark17 Mar 29, Dear wonderopolis, Hi I think 13 is bad luck at certain times.

I think friday the 13th is bad luck. I think it is not bad luck when you have to use it or it's your sports number it's like the number 6, which is the devil's favorite number, and if you go to a store and you have to pay 66 dollars and 66 cents it would be bad luck.

Team Clark 11 Mar 29, This wonder was very interesting. I never knew that airplanes skip the 13th row. I also never knew that the fear of thirteen is most common in Western cultures.

I wonder if there is a phobia for everything? Super natural events can be scary sometimes. If everyone had bad luck on Friday the 13th and everyone lost there jobs or got sick it would be a conundrum for everyone. TeamClark23 Mar 29, Hello Wonderopolis, I really like this wonder! I think it's fun learning about different phobias.

In my class we are learning the suffix phobia and today I learned Triskaidekaphobia in class. I wanted to learn more so I checked Wonderopolis. A few questions I had as I was reading were: Why do planes skip the 13th row?

What is the most common and the most least common phobia? I know that this question is a conundrum so you don't have to answer this question. I learned that some people have phobophobia fear of phobias and that there is a phobia with its own name: paraskevidekatriaphobia. Team Clark 18 Mar 29, Hello I thought this wonder was wonderful.

I didn't know that triskaidekaphobia was a real phobia. I had no idea hotels and tall buildings skip the 13th floor. And that planes don't have a 13th row. I wonder if there's a phobia of air?

If the Friday 13 superstition was real, everything would be pandemonium. TeamClark 15 Mar 29, Why are people so much more worried about Friday the 13th than on any other day of the week the 13th lands on? I do not have triskaidekaphobia at all. All the superstitions listed were probably made to just scare people.

I can't believe hotels skip the 13th floor! I never knew there was a word that meant "fear of clowns": coulrophobia. Thank you for making me wonder! Team Clark 1 Mar 29, Hi Wonderopolis, Some of the stuff about the number 13 I didn't know of, like they don't use the number 13 on planes, hotels and other things and people also feel the number 13 is lucky.

We are also learning about phobias and, the number 12 is lucky and here are some 12 days in a month, 12 in a dozen, 12 gods [there was 13 but a god betrayed them and that's interesting]. Here is one thing about the number Apollo 13 which, could have been a conundrum, but they made it back.

Did you know that? I think the number 13 is lucky. Thanks for the info and see you later on a other topic. Team Clark 8 Mar 29, Hello Wonderopolis, This wonder is so cool. I have always wanted to know why Friday the 13 was feared. And now I know. We are learning about phobias at school. It also seems as if unexplained fears surrounding the number 13 are a primarily Western construct. Some cultures, including the Ancient Egyptians , actually considered the number lucky, while others have simply swapped numbers as the base of their phobias— 4 is avoided in much of Asia , for example.

According to the Stress Management Center and Phobia Institute in Asheville, North Carolina, more than 80 percent of hi-rise buildings in the United States do not have a 13th floor, and the vast majority of hotels, hospitals and airports avoid using the number for rooms and gates as well. But if you see something that doesn't look right, click here to contact us! Twice a week we compile our most fascinating features and deliver them straight to you.