Question

By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.

What is the 10 001st prime number?

some methods of finding

Answer 1

wait ok no forget that!! start over

Answer 2

http://www.sosmath.com/tables/prime/prime.html

Answer 3

to test if 'n' is a prime :-
you need to test all the prime numbers < sqrt(n)

Answer 4

this is more of a math/ computer algorithm question, need to find efficient ways of adding primes to list

Answer 5

yeah ganeishi but just

Answer 6

i realized 13 wasnt given it was found so, what would you suggest best way if you just must find the prime too

Answer 7

there will be primes that differ by 2 : (11, 13), (17, 19)

Answer 8

so, we need to test each and every ODD number

Answer 9

is there better way, that is lots of function time

Answer 10

let me get this clear :-
you're saying testing for prime factors < sqrt(n) is a lot of function time ?

Answer 11

no

Answer 12

n is not given

Answer 13

oh, basically u want to create list of all prime number ?

Answer 14

yeah

Answer 15

@mukushla is here :)

Answer 16

but i see what u are suggesting that is not a bad way to go about it too

Answer 17

take every odd number sqrt it and keep checking permutations of our existing prime list?

Answer 18

nope.
just check if a 'single' prime factor exists thats less than sqrt of it

Answer 19

ok so say for 13

Answer 20

if \(n\) is not a prime , there will be atleast one prime factor < \(\sqrt{n}\)

Answer 21

id do 13 mod 2
13 mod 3

Answer 22

if both not 0 then 13 is prime?

Answer 23

yup !

Answer 24

okay this looks like a good idea

Answer 25

can you think of anything more efficient than this

Answer 26

i will write up that program meanwhile brb

Answer 27

nope,
this is also called seive of eratosthenes or something...

Answer 28

cool

Answer 29

good luck wid the program :)

Answer 30

you know python btw ganeshi?

Answer 31

i can understand python
but im good wid perl

Answer 32

oh ive seen this langueage

Answer 33

i didnt know it was popular

Answer 34

python is popular in academics area
perl is popular in work place

Answer 35

both we use...

Answer 36

how about matlab

Answer 37

we dont use matlab much, we have other simulation software

Answer 38

i feel like matlab is really good for all the math stuff, but im not that fluent yet at manipulating matrices

Answer 39

so i stick to writing on python for now

Answer 40

just getting used a new language takes a while

Answer 41

yah. its like, u will be using python for preparing input to matlab... cuz in python manipulating data is easy

Answer 42

@ganeshi8 i think my code is really bad or something lol it takes a while for this to excecute

Answer 43

@ganeshie8

Answer 44

show me the code...

Answer 45

y=[2]
for i in range(1,60000):
a=2*i+1
b=round(a**0.5)
count=0
for j in y:
if j<b:
if a%j!=0:
count=count
else:
count=count+1
if count==0:
y.append(a)

Answer 46

y[10000] doest seem to be giving me the 10 001st prime either hmm

Answer 47

some funky stuff going on i checked the numbers im getting any it seems like they are all prime numbers but some of the numbers are missing or something

Answer 48

y[1001] = 7723

Answer 49

what below line is doing ?

a=2*i+1

Answer 50

but from this chart is the 980th prime
http://www.sosmath.com/tables/prime/prime.html

Answer 51

rounding

Answer 52

let me get rid of that round

Answer 53

yeah

Answer 54

i asked it for primes less than 10
why it is throwing out 11, 13, 17, 19 ?

Answer 55

no for 10

Answer 56

you are looking at all the odd numbers till 21

Answer 57

yeah, why ?

Answer 58

i dunno lol i just coded it that way

Answer 59

i wanted to just enter some numbers to get atleast 10000 primes

Answer 60

oh, thats intentional is it... okay :)
but it seem ot be working fine

Answer 61

but something is wrong
i dunno if there are some reapting primes in there or somethjing

Answer 62

because when i do y[10000] im not getting the right answer

Answer 63

or when im doing y[1000] its really only giving me the 980th prime

Answer 64

okay, let me have a good look at the code again

Answer 65

i took of the round maybe this fixes it let me see

Answer 66

nope still getting 104021

Answer 67

found the issue

Answer 68

whats wrong with it

Answer 69

try this :-

y=[2]
for i in range(1,50):
a=2*i+1
b=round(a**0.5)
count=0
for j in y:
if j<=b:
if a%j!=0:
count=count
else:
count=count+1
if count==0:
y.append(a)

print y

Answer 70

if \(n\) is not a prime , there will be atleast one prime factor \(<\color{red}{=} \sqrt{n}\)

Answer 71

lol i gave u incorrect info before :|

Answer 72

this is fine that wont change my code i think

Answer 73

just really weird how can there be extra numbers popping up

Answer 74

some of them must not be primes in there but wheres that mistake coming from

Answer 75

that changes everything

Answer 76

oh

Answer 77

if u dont put that equal sign,
49 is also a prime according to ur code.

Answer 78

ohhh I see!!

Answer 79

ur code wont check the prime factor 7, for 49

Answer 80

i seee i seeeeeee

Answer 81

<3

Answer 82

cool :)

Answer 83

i thought i already had hte equal there

Answer 84

hard to notice these changes lol

Answer 85

yahh how much time its taking when u iterate ofr 60000 ?

Answer 86

sweet its right

Answer 87

like 15 secs

Answer 88

gives me about 11301 primes for 60000

Answer 89

man.. finding primes must be some advanced math.. i wonder what kind of algorithms they use to find those huge primes

Answer 90

for every aditional digit in my range my time is going up exponentially or cubing

Answer 91

yeah primes get rarer and rarer...

Answer 92

after you solve it it gives you their method, usually the most efficient method u wanna see it?

Answer 93

yesss

Answer 94

they actually did do something we did, this makes me happy

Answer 95

but i dont think it wil be any different from your method :o