Question

Find an interval of 37 consecutive composite numbers.

Answer 1

composites->opposite of prime numbers.
so, in otherwords, we need to find two prime numbers that are separated by 37 numbers.
p1 - >p
p2 -> p+38

Answer 2

@Hoa

Answer 3

so, what happens next

Answer 4

I aint no number theorist. so, here is my cheat
http://en.wikipedia.org/wiki/Prime_gap

Answer 5

@electrokid can I get back my medal? LOL

Answer 6

this is still to difficult to understand

Answer 7

what two prime numbers are 38 numbers away?

Answer 8

@Hoa :'(

Answer 9

atleast I could get the motor started

Answer 10

you seem to be stydying some hardcore math here....

Answer 11

wahh

Answer 12

You cheat, LOL. just joking.!! you deserve more than medal, pal

Answer 13

think you can give me a hint? I might know something but not able to ope the doors in my brain

Answer 14

@mathsucksalot123 which grade are you?

Answer 15

sophomore in college

Answer 16

which course do you take for the problem?

Answer 17

elementary math for teachers

Answer 18

ok..
duh
factorials!!!!
lets forget primes and get back to composites

Answer 19

ah ahah... future mathematician?

Answer 20

barely

Answer 21

remember someone asked the question of
if (50!-31) is prime or composite?

Answer 22

nope

Answer 23

wahh help me, I'm poor

Answer 24

@mathsucksalot123 no help for a professional mathematician here. do it by yourself. you are better than me. no , no help hihihi

Answer 25

no

Answer 26

well,
\[(a!-n)\] will be composite if n > 1 and a>1

Answer 27

just joke,, let eletrokid helps you. I am dummy here

Answer 28

if n-1, the chances of ( a!-1 ) being a prime increase dramatically

Answer 29

get it?

Answer 30

@Hoa @mathsucksalot123

Answer 31

you guys follow?

Answer 32

I am reading and try to understand

Answer 33

this is beautifu

Answer 34

math is not beautiful

Answer 35

@mathsucksalot123 yes, it is.

Answer 36

http://openstudy.com/users/electrokid#/updates/514a5ddae4b05e69bfac3953

Answer 37

asked by this mr. @mathsucksalot123

Answer 38

Ms.

Answer 39

thank you very much

Answer 40

aah. :D

Answer 41

classic male chauvinism

Answer 42

im a girl. can we finish the problem now :)

Answer 43

so, you guys follow where I am getting at?

Answer 44

no

Answer 45

ok,
in the above given link, I explained how (50!-31) is a composite

Answer 46

yea but this is the 37 consecutive composite question

Answer 47

following the same lead,
I can say at 50!-1 CANOOT be a composite

Answer 48

no proof.. but assume.. Proof would be using one of Fermat's theorems.. (lets not go there)

Answer 49

follow that one?

Answer 50

i can't think.

Answer 51

remember why 50!-37 is a composite?

Answer 52

no

Answer 53

ehm, coz, 37 is a factor of the number.
similarly, 45!-3 is a composite with a factor of "3"
23!-6 is a composite with a factor of "6"

Answer 54

yea

Answer 55

so, what about 35!-1 ?
what can be the factor of this one?

Answer 56

anything up to 35

Answer 57

no.. for anything...
that is why \((a!-n)\) is composite \(\forall 1<n<a\)

Answer 58

when n=1, we hopefully get a prime.

Answer 59

can you please just give me the answer. I want to sleep :(

Answer 60

now, we need 37 prime composite numbers in a sequence...

so,
38!-1 ->prime
38!-2 -> composite
38!-3 -> composite
.
.
.
38!-36-> composite
38!-37 -> composite
38!-38 = 37!-1 = prime again

Answer 61

yay me

Answer 62

so, the number of composites in the middle is "37"

Answer 63

whats the answer

Answer 64

THATS the answer!!!!!

Answer 65

type the answer again

Answer 66

all those 37 numbers I just elaborated so nicely

Answer 67

write it without the primes and how i should write it on my paper

Answer 68

you kiddin me!!!!
even the computer you are using will die trying to evaluate the first number!
just write them in factorial format

Answer 69

its consecutive composite. not prime composite. unless those are the same thing

Answer 70

there is no such thing as a "prime composite"
natural numbers (i.e., numbers from +1 to +infinity) are of two types
either a prime or a composite

Answer 71

consecutive, in english, means .. in sequence

Answer 72

OMG just write exactly what i have to write on my paper

Answer 73

and if you see my answers, they are in a sequence.

Answer 74

INTERVAL. i dont think my teacher wants all of that

Answer 75

write 38!-2, 38!-3, ..., 38!-36 and 38!-37
you can put the dots in there.. it is a common practice to mean follow the sequence

Answer 76

I never saw natural numbers written in interval notation... that is for "Real numbers"

Answer 77

ok thanks.

Answer 78

yer welcome